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Development of Surrogates for Aviation Jet Fuels
by
Seyed Ali Nasseri
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied ScienceGraduate Department of Aerospace Studies
University of Toronto
Copyright c© 2013 by Seyed Ali Nasseri
Abstract
Development of Surrogates for Aviation Jet Fuels
Seyed Ali Nasseri
Master of Applied Science
Graduate Department of Aerospace Studies
University of Toronto
2013
Surrogate fuels are mixtures of pure hydrocarbons that mimic specific properties of a real
fuel. The use of a small number of pure compounds in their formulation ensures that
chemical composition is well controlled, helping increase reproducibility of experiments
and reduce the computational cost associated with numerical modeling.
In this work, surrogate mixtures were developed for Jet A fuel based on correlations
between fuel properties (cetane number, smoke point, threshold sooting index (TSI),
density, viscosity, boiling point and freezing point) and the nuclear magnetic resonance
(NMR) spectra of the fuel as a measure of the fuel’s chemical composition. Comparison
of the chemical composition and target fuel properties of the surrogate fuels developed
in this work to a Jet A fuel sample and other surrogate fuels proposed in the litera-
ture revealed the superiority of these surrogate fuels in mimicking the fuel properties of
interest.
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Acknowledgements
There are a number of people without whom this thesis might not have been written,
and to whom I am greatly indebted. I must first express my gratitude towards my su-
pervisor, Professor Omer L. Gulder, who trusted me with this project and provided me
with the opportunity to develop my research skills. I would also like to express my very
great appreciation to Professor Gottlieb for acting as my secondary thesis examiner and
providing detailed comments on my work.
I would like to thank the University of Toronto Institute for Aerospace Studies for pro-
viding me with a productive environment to work in. This work would not have been
possible without the support of all UTIAS staff members and professors who helped me
in my personal and professional growth during the course of my studies at UTIAS. I
would like to offer my special thanks to the student members of the combustion and
propulsion group who helped create an efficient, highly productive and collaborative re-
search environment.
Finally, I want to thank my parents and siblings for instilling in me confidence and a
drive for pursuing my master’s degree.
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Contents
Contents vi
List of Figures vii
List of Tables viii
1 Motivation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Limitations of Real Fuels for Research Applications . . . . . . . . . . . . 1
1.3 Overcoming the Limitations of Real Fuels for Research Purposes . . . . . 3
1.4 Classification of Surrogate Mixtures . . . . . . . . . . . . . . . . . . . . . 4
1.5 General Procedure for Surrogate Fuel Formulation . . . . . . . . . . . . . 5
1.6 Fuel Properties Targeted in Surrogate Fuel Formulation . . . . . . . . . . 6
1.7 A Review of Surrogate Fuel Development Activities . . . . . . . . . . . . 8
1.8 Objectives of the Current Research Work . . . . . . . . . . . . . . . . . . 10
2 Target Fuel Properties 12
2.1 Typical Aerospace Fuel Properties and Standards . . . . . . . . . . . . . 12
2.2 Properties of the Jet A Sample . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Temperature Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Properties of the Target Fuel . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Regression Analysis Procedure 17
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Regression Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Multiple Linear Regression . . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 Nonlinear Regression Analysis . . . . . . . . . . . . . . . . . . . . 18
3.3 Regression Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Coefficient of Determination (R2 Value) . . . . . . . . . . . . . . 20
iv
3.3.2 Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.3 Predicted Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.4 Root Mean Square Error . . . . . . . . . . . . . . . . . . . . . . . 21
4 Correlation Development for Fuel Parameters 22
4.1 Chemical Structure and Nuclear Magnetic Resonance (NMR) Spectroscopy 22
4.1.1 Chemical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.2 Nuclear Magnetic Resonance (NMR) Spectroscopy . . . . . . . . 23
4.1.3 Identifying Chemical Characteristics of Compounds and Mixtures
Using NMR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Cetane Number (CN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Ignition Quality and the Cetane Number . . . . . . . . . . . . . . 27
4.2.2 Cetane Number Measurement . . . . . . . . . . . . . . . . . . . . 28
4.2.3 Sources of Cetane Number Data . . . . . . . . . . . . . . . . . . . 29
4.2.4 Correlations Development for Cetane Number . . . . . . . . . . . 30
4.2.5 Correlation of Cetane Number with NMR Spectrum . . . . . . . . 31
4.3 Sooting Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.2 Effect of Chemical Structure on Sooting Tendency . . . . . . . . . 35
4.3.3 Sooting Tendency Indices . . . . . . . . . . . . . . . . . . . . . . 37
4.3.4 Correlations Developed for Sooting Tendency . . . . . . . . . . . 41
4.3.5 Correlation Development Between Sooting Tendency and Proton
NMR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.2 Density Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.3 Boiling Point Correlations . . . . . . . . . . . . . . . . . . . . . . 50
4.4.4 Freezing Point Correlations . . . . . . . . . . . . . . . . . . . . . 53
4.4.5 Dynamic Viscosity Correlations . . . . . . . . . . . . . . . . . . . 54
5 Application of the Correlations to Jet Fuel and Its Surrogates 57
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 NMR Spectrum of Jet Fuel and Its Surrogates . . . . . . . . . . . . . . . 57
5.3 Properties of Jet Fuel and Its Surrogates . . . . . . . . . . . . . . . . . . 58
6 Surrogate Mixture Development 62
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
v
6.2 Mixture Formulation Algorithm . . . . . . . . . . . . . . . . . . . . . . . 62
6.2.1 Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2.2 Algorithm Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2.3 Definition of Different Cases . . . . . . . . . . . . . . . . . . . . . 65
6.3 Mixture Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7 Conclusion 72
Appendices 74
Bibliography 80
vi
List of Tables
1.1 Chemical compositions of some of the surrogate fuels proposed for jet fuel. 11
2.1 Chemical composition of Kerosene, JP-8 and Jet A. . . . . . . . . . . . . 13
2.2 Properties of aviation jet fuels cited in different sources. . . . . . . . . . . 14
2.3 Aviation jet fuel specifications and statistical data. . . . . . . . . . . . . 14
2.4 Target values for mixture properties. . . . . . . . . . . . . . . . . . . . . 16
4.1 Ranges of chemical shifts and their corresponding functional groups. . . . 26
4.2 Statistical properties of some of the correlations proposed for CN. . . . . 32
4.3 Statistical properties of the regression models developed for CN. . . . . . 33
4.4 Correlations proposed for sooting tendency indices. . . . . . . . . . . . . 41
4.5 Statistical properties of the regression models developed for smoke point. 43
4.6 Statistical properties of the regression models developed for TSI. . . . . . 45
4.7 List of some of the QSPRs proposed for thermophysical properties of interest. 48
4.8 Statistical properties of the regression models developed for density. . . . 49
4.9 Statistical properties of the regression models developed for boiling point. 51
4.10 Statistical properties of the regression models developed for freezing point. 53
4.11 Statistical properties of the regression models developed for viscosity. . . 55
5.1 NMR spectra of the Jet A sample and several jet fuel surrogates. . . . . 59
5.2 Application of the correlations to jet fuel sample and its surrogates. . . . 60
5.3 Properties of jet fuel surrogate fuels calculated using mixture rules. . . . 61
6.1 Chemical composition of jet fuel surrogates developed in this work. . . . 70
6.2 NMR spectra of the proposed aviation jet fuel surrogates and Jet A fuel. 71
6.3 Properties of Jet A and surrogate fuels developed in this work. . . . . . . 71
7.1 Chemical composition of the best surrogate fuels developed in this work. 73
A.1 Coefficients for linear correlations presented in Chapter 4. . . . . . . . . . 75
A.2 Coefficients for artificial neural network models presented in Chapter 4. . 76
vii
List of Figures
4.1 Complete proton NMR spectrum of the Jet A fuel. . . . . . . . . . . . . 24
4.2 Cetane number regression results. . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Cetane number regression results compared to several proposed correlations. 34
4.4 Regression analysis results for smoke point. . . . . . . . . . . . . . . . . . 43
4.5 Diffusion flame TSI regression analysis results. . . . . . . . . . . . . . . . 45
4.5 Diffusion flame TSI regression analysis results. . . . . . . . . . . . . . . . 46
4.6 Comparison of diffusion flame TSI regression results to correlations pro-
posed in the literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.7 Density regression results. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.8 Boiling point regression analysis results. . . . . . . . . . . . . . . . . . . 52
4.9 Comparison of the ANN4 boiling point model to correlations proposed in
the literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.10 Freezing point regression analysis results. . . . . . . . . . . . . . . . . . . 54
4.11 Dynamic viscosity regression analysis results. . . . . . . . . . . . . . . . . 56
6.1 Algorithm used for surrogate mixture formulation. . . . . . . . . . . . . . 66
6.2 Definitions of cases for surrogate mixture formulation. . . . . . . . . . . . 67
A.1 The ANN as depicted by the MATLAB documentation. . . . . . . . . . . 74
viii
Chapter 1
Motivation
1.1 Introduction
Surrogate fuels are chemical mixtures developed using pure compounds as a replacement
for real fuels for research, modeling and simulation purposes. They are blended to mimic
specific properties of the real fuel. In this chapter, methods for surrogate fuel formulation
will be reviewed and some of the results from previous research on this topic will be
presented.
1.2 Limitations of Real Fuels for Research Applica-
tions
Understanding the detailed chemistry, combustion behavior and flow properties of con-
ventional and alternative fuels is of grave importance in the efficient utilization of these
fuels in combustion and propulsion systems. However, the chemistry of these real fuels
is extremely complicated, limiting the amount of insight that can be gained by directly
using them in combustion studies. Not only do they typically contain many different
chemical species, but their composition varies depending on the source of the crude oil
and the refining process.
Most transportation fuels are complex mixtures of thousands of hydrocarbons includ-
ing linear and branched alkanes, cycloalkanes, alkenes and aromatics [1, 2]. Additives
might also be added in low concentrations to such fuels to improve performance and fuel
stability. For instance, the main component of jet fuels is kerosene with major species
including straight chain and branched chain alkanes (35-45 % volume), cycloalkanes (30-
35% volume), aromatics (one and two ring, 20-25% volume) and alkenes (less than 5%
1
Chapter 1. Motivation 2
volume) [1]. Jet fuel additives include naphtas which are added to jet fuels to improve
their performance. JP-8, one of the military variant of jet fuels, is often prepared by
splash blending from base Jet A stock at the end-user tank and includes icing inhibitors,
corrosion/lubricity enhancers, and anti-static additives.
The physical properties of a fuel (such as vapor pressure and flash point) and its com-
bustion properties (such as octane or cetane numbers and smoke point) are dependent
on the composition of the fuel. The fuel composition itself is greatly variable, depending
on manufacturer, feedstock origins, season, and economic factors that are imposed by
the refinery [1, 3, 4]. This variability in composition of the fuel is a hurdle to conducting
meaningful combustion studies using real fuels.
Fortunately, several means have been developed to overcome the problem of variable
composition and its effect on combustion studies. For some fuels, such as gasoline, refer-
ence mixtures have been developed as consensus standards which scientists and engineers
can use in their experiments. For example, a commonly used surrogate for gasoline fuels
contains iso-octane and n-heptane [2]. The availability of such standard mixtures ensures
that all experiments are conducted using a well-understood fuel. Unfortunately, there are
no set of consensus standard mixtures for jet fuels. Reasons for this include the diversity
of testing protocols for gas turbine fuels and the unavailability of a knowledge base (such
as detailed kinetic mechanisms) for some of the components of real jet fuels.
In the past, many important trends in gas turbine combustor aerodynamics could be
established using gaseous propane as the fuel [5]. However, the need for simulating com-
plex properties of the fuel such as emissions, flame stability and combustor durability
plus the need to improve key emerging propulsion technologies make such simple models
less robust for modern applications. Hence, more robust models need to be developed
based on mixtures of hydrocarbons.
The variable composition of fuels also affects computational modeling. Not only are real
fuels complex to model, but the models developed for one batch of fuel can not be used
for another batch due to the variability in chemical composition. Validation of such com-
putational models also requires experimental data using the real fuel.
These issues can be resolved by using standardized fuels. The use of standardized fuels
for modeling and experimentation increases experimental reproducibility and model gen-
erality. Moreover, the same standard fuel can be tested in different experimental settings,
geographical locations and using different analysis techniques.
Some might argue that standard mixtures may be developed using refinery streams.
Even if such standardized fuels are blended from refinery streams and stored for later
use, there is only a finite volume of them available, and they could chemically deteriorate
Chapter 1. Motivation 3
over time [6]. It is practically impossible to recreate exactly the same mixture with the
same chemical composition from refinery streams. Furthermore, to reduce the need for
experimental testing and optimization of engines, acceptable modeling capability for fuels
is necessary. Due to the large number hydrocarbons in fuels from refinery streams, use of
such fuels in simulations is impractical. In addition to the change in composition of such
fuels, kinetic models for such fuels are unavailable since all the fundamental data needed
for development of such a model (e.g., chemical kinetic rate constants, reaction paths,
thermodynamic parameters) are not available and interactions between fuel components
are not well understood [7]. The high computational cost in terms of CPU and memory
usage required for a fully detailed chemical kinetic descriptions of hydrocarbon oxidation,
tracking of hundreds of chemical species and thousands of reaction steps is an additional
factor prohibiting the use of real fuels in CFD simulations [6, 8]. Hence, reproducible
standardized fuels blended from pure compounds are the only viable way to overcome all
these issues.
1.3 Overcoming the Limitations of Real Fuels for Re-
search Purposes
A solution to the problems outlined in the previous section is the use of surrogate fuels. It
is generally agreed in both experimental and numerical settings that the most important
traits of fuels can be effectively reproduced by simpler fuel surrogates containing a limited
number of components of high purity [1, 2, 3, 4, 6, 9, 10, 11]. This approach controls and
monitors fuel composition accurately, allowing for well-controlled fundamental modeling
and experimental studies in combustion. The smaller number of fuel components involved
means that experiments with these surrogates are more reproducible, facilitating deeper
insights into combustion processes. In addition to providing a model fuel for studying
the effect of fuel properties and chemical composition on combustor performance, the
compositional control afforded by a surrogate fuel is attractive for the development and
verification of computational codes for combustor design. Obviously, such surrogates are
not replacements for the real fuel for engine verification purposes and may only be used
for modeling and design purposes.
An inherent limitation of using surrogate mixtures is that they are often developed for
modeling specific properties of the fuel or specific combustion processes and ,hence, lack
generality. For example, a mixture developed to represent thermophysical parameters
Chapter 1. Motivation 4
might not be the best mixture to model the sooting behavior of the fuel. Moreover, large
kinetic models for surrogates might still contain thousands of species and reactions. Such
models can usually only be used for simulating simple homogeneous systems and must
be reduced for multidimensional engine applications [2]. It has also been suggested that
properties relying on trace amounts of specific compounds might not be modeled with the
required precision by surrogate fuels. For example, thermal stability and emissions are
affected by trace amounts of polar compounds (such as sulphur containing compounds)
and metal content of the fuel [10] which are usually not included in surrogate fuels.
1.4 Classification of Surrogate Mixtures
Surrogate fuels can be classified either based on the properties they can model or based
on the number of components used in their formulation. Surrogate fuels are usually
classified into two groups based on the properties they model:
• Physical surrogate fuels.
Mixtures which are used to mimic physical properties of the fuel such as density,
viscosity and volatility.
• Chemical surrogates.
Such surrogate fuels are formulated to have the same chemical compositions and
average molecular mass as the fuel. Such mixtures should be composed of species
with the same chemical class as the main components of the fuel [12]. Theoretically,
they should have chemical properties similar to the fuel under study.
The type of surrogate fuel developed and the parameters considered in creating the sur-
rogate fuel depend on its application. For instance, thermophysical properties such as
density, viscosity, thermal conductivity and specific heat are more important in heat
transfer analysis, while for analyzing phase changes and phase behavior, boiling point
and distillation curve become important. While surrogate fuels are often formulated
based on the ability of a particular mixture to reproduce specific properties of the fuel,
there is usually a desire to develop surrogate fuels that have secondary physical and
chemical properties similar to the finished fuel.
The number of components used in formulating the surrogate varies based on the appli-
cation of the surrogate. Single component surrogates have been used to analyze com-
bustion efficiency [7]. Two-component surrogate fuels have been able to predict many
combustion properties of jet fuels. Such surrogate fuels are usually made of a long chain
Chapter 1. Motivation 5
aliphatic compound (usually n-decane or n-dodecane) and a cyclic compound (trimethyl-
benzene, propylbenzene, methylcyclohexane, decalin and 1-methylnaphthalene) [12]. For
chemistry dependent or more detailed modeling of chemical or physical properties, more
components are added. Specific number of components have been suggested in the litera-
ture for modeling some combustion processes [10]. The exact number of species needed to
model all aspects of combustion is not yet known [7]; however, most proposed surrogate
fuels have 4-14 components [13] and 3-10 components have been suggested to suffice for
most applications [14]. In most cases, a compromise is reached between the degree to
which specific combustion properties are simulated and the number of components used
in the mixture.
1.5 General Procedure for Surrogate Fuel Formula-
tion
Different procedures have been proposed for formulating surrogate fuels [10, 15, 16, 12].
Taking into account such proposed procedures, the following general steps need to be
followed:
1. Chemical analysis of the parent fuel to identify chemical composition.
2. Choosing the aspect of combustion the surrogate fuel is supposed to model.
3. Developing a methodology for surrogate fuel formulation, for example hydrogen to
carbon ratio matching.
4. Construction of a list of tentative species for use in the surrogate fuel formulation
which represent the various families of hydrocarbons available in the parent fuel.
5. Blending the components selected based on the methodology to match fuel compo-
sition (10-15 hydrocarbons maximum).
6. Comparing the physical and chemical properties of the surrogate with the parent
fuel and iterating until an acceptable degree of similarity is reached.
The fourth step above requires the creation of a database of tentative species for use in
surrogate fuel formulation. The following guidelines have been proposed to assess the
suitability of chemical species for use in surrogate fuel formulation for jet fuels [10, 15, 16]:
Chapter 1. Motivation 6
• Feasibility and availability of experimental data.
Chemical kinetic mechanisms should be available for the species used in the sur-
rogate fuel. Priority should be given to compounds for which the most abundant
and reliable experimental data are available.
• Simplicity.
Species with low number of carbons should be used. Typical guidelines are normal
alkanes with less than 12 carbons, mono-cyclic alkanes with less than 8 carbons
and simple aromatics.
• Similarity.
In most cases, the component should have some similarity with the fuel being
modeled in terms of target properties.
• Availability and low cost.
1.6 Fuel Properties Targeted in Surrogate Fuel For-
mulation
One reason for the large variation in surrogate fuel composition is the wide variety of
jet fuel applications, and the sensitivity of these applications to mixture composition. In
order to determine the best composition for a surrogate fuel, the purpose for developing
the surrogate fuel needs to be specified first. Parameters that need to be predicted ac-
curately (target parameters) need to be identified, along with accuracy levels for each of
these parameters. Different research groups have used different parameters in developing
surrogate fuels. Such parameters have included chemical composition, distillation curve
properties, ignition quality, sooting tendency and many different thermophysical proper-
ties.
One of the primary steps in surrogate fuel development is quantifying chemical com-
position. Different measures of the chemistry of the fuel have been used in developing
surrogate fuels. Fuel properties stem from the chemistry of the fuel and strong correla-
tions have been observed between specific chemical species and properties of the fuel. For
instance, soot and other pollutant formation strongly depend on the amount of aromatic
rings and unsaturated compounds present in the fuel. As a result, many surrogate fuel
formulation procedures have some measure of chemistry as one of their target parameters.
Measures of chemical composition may include:
Chapter 1. Motivation 7
• Hydrogen to carbon ratio which is a measure of the degree of saturation of the fuel.
It affects local mixing phenomena in terms of the stoichiometry, flame speed, flame
temperature, and heat of combustion [2, 4, 17].
• Aromatic content.
• Chemical composition of the fuel measured using spectroscopic techniques.
Since the aim of developing surrogate fuels is modeling combustion phenomena, com-
bustion properties have also been used as targets in surrogate fuel formulation. These
include ignition quality which affects engine startability and operations, and sooting ten-
dency which affects engine emissions, flame propagation and combustion chamber life.
Thermophysical properties affect fluid flow and the formation of the air/fuel mixture.
Thus, they have also been used as target parameters for surrogate fuel formulation, spe-
cially for heavy fuels such as jet fuels. Thermophysical properties used for surrogate fuel
formulation include:
• Density which affects the atomization and mixing processes in propulsion systems.
It has been shown that many thermophysical properties of petroleum products (such
as specific heat capacity, latent heat of vaporization, and thermal conductivity) are
closely related to fuel density and can be accurately estimated using it[4]. It should
be noted that density is known to be less sensitive to fuel composition [18].
• Fuel’s heating value or enthalpy of combustion [1, 14].
• Volatility (distillation properties, vapor pressures, or boiling point) which affects
pre-combustion processes in combustion chambers [14] and provides valuable insight
into the performance of engines [4].
• Viscosity [1] which affects pre-combustion processes in combustion chambers with
short propellant residence times and high efficiency requirements [14]. Viscosity is
highly sensitive to both chemical composition and temperature [3].
• Thermal stability [1].
• Surface tension which affects fuel atomization and mixing [14].
• Molecular mass (indirectly linked to distillation curve) [2, 17].
• Diffusion coefficients [6].
Chapter 1. Motivation 8
• Speed of sound which may be used for measuring fuel levels in aircraft fuel tanks.
This property is slightly sensitive to fuel composition [18].
It should be emphasized that many of the targeted properties might be interrelated.
For instance, increased aromatic content in the fuel may lead to higher emissions [19].
Moreover, many of these properties such as density, heat release, volatility, viscosity and
thermal stability are regulated by fuel specifications.
1.7 A Review of Surrogate Fuel Development Activ-
ities
Many surrogate fuels have been developed based on different applications and number
of components. There are currently active working groups for developing experimental
databases and surrogate models for modeling jet, diesel, and gasoline fuels. A good exam-
ple of such collaborative work is the “Fuels for Advanced Combustion Engines” (FACE)
initiative [4].
Some of the previous research in this area focused on surrogate fuels with applications
in modeling jet fuel pool fires. Violi et al. [15] developed a surrogate fuel for pool fire
modeling by matching sooting properties and boiling point distribution of the actual fuel.
Eddings et al. [9] used relatively inexpensive components with known chemical kinetics
which were representative of the main classes of hydrocarbons present in jet fuels to
develop surrogate fuels with less than 10 components which matched the volatility, flash
point, sooting tendency, heat of combustion and flame characteristics of Jet A/JP-8 pool
fires.
Surrogate fuels have also been used for modeling specific combustion characteristics of
fuels. Aksit et al. [5] developed binary mixtures of alkanes and mono-aromatic com-
pounds to mimic the sooting propensity of kerosene and used this for detailed kinetic
modeling in CFD simulations. Hernandez et al. [20] developed a diesel fuel surrogate
for improving ignition modeling capability in HCCI engines by merging n-heptane and
toluene kinetic mechanisms.
Researchers have also focused on targeting specific fuel properties and using empirical
equations, mixture rules and equations of state in surrogate fuel formulation. Androulakis
et al. [21] developed a numerical algorithm based on integer programming that facilitates
the definition of model diesel fuels from well-characterized chemical streams while mini-
mizing the number of components. They focused on volatility range, ignition character-
istics (octane or cetane number), elemental composition (sulfur and nitrogen), molecular
Chapter 1. Motivation 9
composition (aromatics and alkenes) and vapor pressure as target properties and used
parameters such as the distillation curve, normal alkane content, iso-alkane content, one-
ring cycloalkane content, two-ring cycloalkane content, multi-ring cycloalkane content,
one-ring aromatic content, two-ring aromatic content, cetane number, threshold sooting
index (TSI) and density in their procedure. Huber et al. [22] used a procedure based
on experimental data for density, speed of sound, viscosity and thermal conductivity
along with an advanced distillation curve to develop surrogates for two rocket propel-
lants (RP-1 and RP-2). They also used advanced distillation curve measurements to
improve the volatility characteristics of a surrogate model to better represent thermo-
dynamic properties (density, sound speed, and boiling point) and transport properties
(thermal conductivity and viscosity) of the target fuel [16]. In a separate work, they
used an equation of state in developing a surrogate fuel model to represent the volatility
behavior (distillation curve) of a synthetic paraffinic aviation fuel derived from biomass
[23]. Bruno et al. [18] used an equation of state and a viscosity and thermal con-
ductivity surface for each pure surrogate fuel component to develop surrogate fuels for
jet fuel. Slavinskaya et al. [14] developed a surrogate fuel which closely matched the
boiling-point curve and two-phase diagram of Jet A and had similar physical properties.
Properties such as combustion enthalpy, formation enthalpy, molar mass, approximate
formula, sooting tendency index, critical point, chemical composition, carbon to hydro-
gen (C/H) ratio, flow reactor concentration histories, flame speeds and ignition delays
were compared in their work. Anand et al. [4] developed surrogate models for nine fuels
for the advanced combustion engines using computer simulations of distillation profiles.
They focused on matching specific gravity, lower heating value, hydrogen to carbon ratio
(H/C), cetane number, and cetane index of the fuels.
As fuel chemistry is inherently responsible for all other fuel properties, many researchers
have focused on matching the chemistry of the fuel using different spectroscopic tech-
niques. Natelson et al. [13] developed surrogates for jet and diesel fuels using three
components so that they could capture the three major hydrocarbon classes (alkane, cy-
cloalkane, and aromatic) found at significant levels in jet and diesel fuels, and maintain a
small number of components for computational modeling. Zhang et al. [24] developed a
surrogate fuel for JP-8 by matching its chemical composition measured using C-13 nuclear
magnetic resonance (NMR) spectroscopy. Huber et al. [25] developed a five component
surrogate for JP-900 using only information obtained from a gas chromatography-mass
spectrometry (GC-MS) analysis of the fuel and an advanced distillation curve.
A review of these surrogates shows that reference and model components selected to de-
fine surrogate fuels for jet fuel include normal alkanes (such as heptane, decane, dodecane,
Chapter 1. Motivation 10
tetradecane and hexadecane), branched alkanes (such as isooctane and isocetane), cy-
cloalkanes (such as methylcyclohexane), aromatics (such as toluene, xylenes and methyl-
naphthalene), multi-ring compounds (such as tetralin and Decalin), and alkenes (such as
1-pentene) [1].
A list of some of the Jet A and JP-8 surrogate fuels, for which data relevant to this
project was available, is summarized in Table 1.1. These surrogates will be analyzed
later in this work. It should be noted that some of the promising surrogate fuels such as
those proposed in reference [16] were not included in Table 1.1 due to unavailability of
NMR spectra for their components.
1.8 Objectives of the Current Research Work
After analyzing the target parameters used by different research groups, the following
parameters were chosen as target parameters which should be mimicked by the surrogate
fuel developed in this research project:
• Thermophysical properties including density, dynamic viscosity, initial boiling point,
maximum freezing point.
• Sooting tendency (through smoke point or other sooting tendency indices).
• Ignition quality (represented by cetane number).
• Chemical composition as measured through proton NMR spectra with hydrogen to
carbon ratio (H/C) and molecular mass as auxiliary parameters.
Obviously, such a surrogate fuel will be classified as both physical and chemical. The aim
of this work was to use the minimum number of compounds possible to formulate the
surrogate fuel. Due to the dependance of all fuel properties on the chemical composition
of the fuel, correlations were developed between the chemical composition of the fuel
and its thermophysical properties, sooting tendency and ignition quality parameters.
This simplifies the mixture analysis as it transforms the mixture formulation into a
mathematical problem and makes chemical composition the only fuel parameter included
in mixture formulation.
Chapter 1. Motivation 11
Table 1.1: Chemical compositions of some of the surrogate fuels proposed for jet fuel.
Name Target Fuel Component Type Vol. % Ref.
1 Modified Aachen Surrogate Jet A/JP-8n-dodecane Normal Alkane 80
[3]1,2,4-trimethylbenzene Aromatic 20
2 Aksit Kerosenen-decane Normal Alkane 70
[5]propylbenzene Aromatic 30
3 Eddings JP-8
n-octane Normal Alkane 3.5
[9]
n-dodecane Normal Alkane 40n-hexadecane Normal Alkane 5
decalin Cycloalkane 35xylenes Aromatic 8.5tetralin Aromatic 8
4 Aachen Surrogate Kerosenen-decane Normal Alkane 80
[12]1,2,4-trimethylbenzene Aromatic 20
5 Slavinskaya Jet A
n-dodecane Normal Alkane 20
[14]n-hexadecane Normal Alkane 32
iso-octane Branched alkane 13propylcyclohexane Cycloalkane 10
1-methylnaphtalene Aromatic 25
6 Violi JP-8
n-dodecane Normal Alkane 30
[15]
n-tetradecane Normal Alkane 20isooctane Branched alkane 10
methylcyclohexane Cycloalkane 20m-xylene Aromatic 15tetralin Aromatic 5
7 Drexel S-5 JP-8
n-dodecane Normal Alkane 26
[26, 27]iso-cetane Branched alkane 36
methylcyclohexane Cycloalkane 14decalin Cycloalkane 6
α-methylnaphthalene Aromatic 18
8 Schultz JP-8
n-octane Normal Alkane 15
[28]
n-dodecane Normal Alkane 20n-tetradecane Normal Alkane 15n-hexadecane Normal Alkane 10
iso-octane Branched alkane 5methylcylcohexane Cycloalkane 5
cyclooctane Cycloalkane 5xylene Aromatic 5
butylbenzene Aromatic 5tetramethylbenzene Aromatic 5α-methylnaphthalene Aromatic 5
tetralin Aromatic 5
9 Montgomery JP-8
n-octane Normal Alkane 22.6
[29]n-dodecane Normal Alkane 34.7
methylcyclohexane Cycloalkane 16.7butylbenzene Aromatic 16
10 Humer JP-8n-dodecane Normal Alkane 60
[30]methylcyclohexane Cycloalkane 20xylene Aromatic 20
11 JP-8 surrogate (TSI = 22) JP-8n-dodecane Normal Alkane 54
[31, 32]iso-octane Branched Alkane 181,3,5-trimethylbenzene Aromatic 28
12 Kahandawala JP-8n-heptane Normal Alkane 80
[33]toluene Aromatic 20
Chapter 2
Target Fuel Properties
As mentioned in Chapter 1, target values need to be identified for the target fuel parame-
ters to initiate choosing fuel components and formulating mixtures which mimic the fuel.
It is reasonable to use the assumption of an average fuel in surrogate mixture formulation
[7]. In this chapter, the properties of aviation jet fuel are summarized based on statis-
tical fuel data and data sheets of a Jet A fuel sample available at the Combustion and
Propulsion Group. This information is used to reach target values for fuel properties.
2.1 Typical Aerospace Fuel Properties and Standards
There are several propellants currently in use by the aerospace industry. These include
Jet A (Jet A-1 in Europe), JP-8 (military equivalent of Jet A with an additive package),
Jet B (enhanced cold-weather performance) and RP-1. Recently, several new fuels such
as JP-800, JP-900, Si-3 and S-8 have also been developed. All these fuels are composed
of hundreds of aliphatic and aromatic hydrocarbons. The main component of aviation
jet fuels is kerosene [1].
Aviation turbine fuels are not defined by composition, molecular structure, or purity.
Instead, their characteristics are limited by boundary conditions imposed based on fun-
damental or empirical inspection tests based on solutions to past engine or aircraft prob-
lems [34]. The individual properties of the fuel can be divided rather arbitrarily into bulk
and trace properties [34, 35]. Bulk properties are those that are affected by significant
compositional changes (more than 5% by volume of the total fuel). Trace properties tend
to respond to changes less than 1% by volume or even 1 ppm or less. Energy content,
combustion characteristics, distillation range, density and fluidity depend on bulk fuel
composition while lubricity, stability, corrosivity, cleanliness and electric conductivity
depend on trace amounts of species. Based on this definition, the properties of our in-
12
Chapter 2. Target Fuel Properties 13
Table 2.1: Chemical composition of Kerosene, JP-8 and Jet A (values are volumetricpercentages).
Hydrocarbon Type Kerosene [1] Kerosene [36]Jet A (World
survey average)[7, 13]
JP-8 (JetA/A-1)
[10]JP-8 [33]
Straight Chain andBranched Chain
Alkanes35-45 50-65 58.78 60 60
Cycloalkanes 30-35 20-30 21.22 20 20Aromatics 20-25 10-20 19.94 18 15-20Alkenes 0-5 - 0.06 2 -
terest are bulk properties and the compositional accuracy of our interest is about 5% by
volume.
Aviation jet fuels are kerosene fuels, with a typical boiling range of 160-260 ◦C. Aviation
jet fuel specifications (Jet A, Jet A-1, JP-8) control the 10% point of the distillation
(< 205◦C) and the final boiling point (< 300◦C) [7]. JP-8 is Jet A fuel mixed with a
military additive package that includes an icing inhibitor (1000-1500 ppm), corrosion in-
hibitor/ lubricity enhancer (20 ppm), and a static dissipater additive (5 ppm) [3]. Based
on Table 6.1 which shows the typical compositions of Kerosene, Jet A, Jet A-1 and JP-8
fuels, the assumption of an average jet fuel seems to be reasonable for surrogate mixtures
developed in this work as compositional changes seem to be less than 5% by volume.
Gas chromatography reveals that JP-8 components have 5-35 carbons [33]. The n-
paraffins typically range from n-octane (n-C8) to n-hexadecane (n-C16), with maximum
concentrations from n-decane (n-C10) to n-dodecane (n-C12). These criteria can be used
in assessing chemical similarity of surrogate mixtures to aviation jet fuels and in choosing
suitable components for surrogate mixtures.
Some of the cited properties of aviation jet fuel for different samples are summarized in
Table 2.2. Evidently, the small compositional changes mentioned earlier lead to large
variations in jet fuel properties. Aviation jet fuel specifications also impose limits on
several properties of the fuel. Unfortunately, the specifications can vary and depend on
the country where the fuel is produces or used. Table 2.3 summarizes civil aviation jet
fuel specifications for the US fuel manufacturers and an international checklist, along
with statistical data of Jet A samples from around the world. The international checklist
was developed to facilitate airport operations and takes into account requirements by
different agencies. Hence, it is a reasonable alternative to aviation jet fuel specifications.
It should be note that Canada uses Jet A-1 as specified in the CAN/CGSB-3.23 specifi-
cation [37], which has properties similar to other Jet A-1s. Test methods which are used
Chapter 2. Target Fuel Properties 14
Table 2.2: Properties of aviation jet fuels cited in different sources.
Parameter JP-8 [39] JP-8 [26] JP-8 [36] Jet A/A-1[26] Jet A [36] Kerosene [36]
H/C ratio1.84-2.07
(average 1.9)1.91 1.92 1.91 1.9 1.9-2.1 (C9-C13)
MW (g/mol) 153 153 152 153 162 175 [40]Density (kg/m3) 804 797 - - - 770-830
Aromatic Content (vol%) 20 - - - - 10-20
Cetane Number32-57
(average 44)45 - - - -
Threshold Soot Index (TSI)16-26
(average18-22.1)
- - - - -
Average Formula C11H21 C11H21 C10.9H20.9 C11H21 C11.6H22 -Boiling Point (◦C) - 165-265 Average 204 170-300 Average 216 140-280
Maximum Freezing Point (◦C) - -51 --40 (Jet A),
-47 (Jet A-1)- -
Kinematic Viscosity (cSt) - 1.2 @ 40 ◦C - - - 1.8 @ 15◦C [5]
Table 2.3: Aviation jet fuel specifications and statistical data.
Specifications [26, 34, 35, 38] Statistical Data [41]Country United States International International Jet A Samples
Designation Jet A Jet A-1 Jet A
Specification ASTM D 1655International
ChecklistMin Max Mean Wt Mean
Aromatics (vol%), max 25 22 14.8 21.9 19.15 18.73Naphthalenes (vol%), max 3 1 2.73 2.15 1.9
Sulfur (mass%), max 0.3 0.0545 0.14 0.1142 0.1011Initial Boiling Point (◦C) Report Not ReportedFinal Boiling Point (◦C) 300 263.3 279.3 274.5 270Density (kg/m3), 15 ◦C 775-840 775-830 811.9 816.6 815.6 815.9
Freezing Point (◦C), max 40 -47 -51 -44.8 -48.3 -47.4Kinematic Viscosity
(mm2/sec), max at 20 ◦C8 4.1 5.916 4.53 4.34
Net Heat of combustion(MJ/kg), min
42.8 43.09 43.13 43.11 43.11
Smoke point (mm), min 18 20 19 22 20.8 19.92
in defining the requirements in Table 2.2 are outlined in references [35, 38]. Note that,
based on the statistical data summarized in Table 2.3, sometimes the fuels do not abide
to all specifications.
2.2 Properties of the Jet A Sample
A Jet A sample was acquired by the Combustion and Propulsion Group at UTIAS for
use in this work. Chemical composition of the target fuel is based on the properties of
this fuel, which will be outlined in Chapter 4. Information about other properties of the
Chapter 2. Target Fuel Properties 15
sample was acquired through the sample information sheet (Appendix A in [42]). This
sample had an initial boiling point of 161.5 ◦C, a maximum freezing point of -54.5 ◦C and
a density of 804.8 kg/m3 at 15 ◦C. These are experimentally evaluated values that can
be used in the mixture analysis as properties of the target fuel. Unfortunately, the data
did not include molecular mass, viscosity, cetane number and sooting data of the sample.
All these parameters need to be determined prior to surrogate mixture formulation. The
correlations developed in Chapter 4 will be used for evaluation of the properties not
determined by the fuel data sheet.
2.3 Temperature Corrections
The density and dynamic viscosities used for correlation development in Chapter 4 were
evaluated at 298.15 K. Hence, the density and dynamic viscosity of aviation jet fuel had
to be corrected for temperature. The following correction is suggested for correcting
density for temperature changes over small temperature ranges [43]:
ρ
ρ0
=1
1 + β(T − T0)(2.1)
Where ρ0 is the reference density at the reference temperature T0 and β is the volumetric
temperature coefficients which has a value of 9.9 × 10−4 1/K for aviation jet fuel [35].
The following equation was used for correcting dynamic viscosities [44]:
ln(µ) = A +B
T(2.2)
The values of the constants A and B were evaluated based on aviation jet fuel viscosity
measurement data from reference [45] to be - 8.45 cP and 2489.9 cP/K respectively for
Jet A fuel.
2.4 Properties of the Target Fuel
Based on the properties of most aviation jet fuel samples outlined in this chapter, values
for target fuel properties were chosen, as summarized in Table 2.4. The target values
are used for matching surrogate fuel properties to the real fuel, while the target ranges
are used as constraints in developing surrogate mixtures and for validating correlations.
These target fuel properties are used alongside the proton NMR spectrum of the sample
(outlined in Chapter 4) for surrogate mixture formulation in Chapter 6. All temperature
Chapter 2. Target Fuel Properties 16
Table 2.4: Target values for mixture properties (Correlations used in this table are pre-sented in Chapter 4.).
Property Target Value Source Target Range SourceCetane Number 45 Correlations 32-57 JP-8 [39]
Smoke Point (mm) 21 Jet A[41] > 18 ASTM D 1655Diffusion Flame Threshold
Sooting Index (TSI)26 Correlations 16-26 JP-8 [39]
Density (kg/L) 0.7969 Sample properties [42] 0.7827-0.8483 Kerosene [36]Boiling Point (K) 434 Sample properties [42] 413-443 Table 2.2
Maximum Freezing Point (K) 218.65 Sample properties [42] 215-233.15 Jet A and JP-8 [26]Dynamic Viscosity(cP) 1.6 Correlations < 6.5 ASTM D1655Molecular Mass (g/mol) 153 JP-8 [26, 39] 153-175 Table 2.2
H/C 1.9 JP-8 and Jet A [36, 39] 1.84-2.1 JP-8 [39]
dependent properties were evaluated at a temperature of 298.15 K. It should be noted
that the cetane number, threshold sooting index (TSI) and viscosity of the sample were
determined using correlations which will be presented in Chapter 4. In the case of the
smoke point, the value calculated using these correlations was outside the range of typical
values for aviation jet fuels and has not been used in the target fuel properties. The initial
boiling point of the jet fuel was used since correlations developed in Chapter 4 only apply
to initial boiling points and can not assess other boiling point values.
Chapter 3
Regression Analysis Procedure
3.1 Introduction
As mentioned in the previous chapter, it has been well established that all fuel properties
are a function of the chemical composition, degree of saturation (as identified using the
H/C ratio) and molecular mass . Hence, it is possible to correlate the NMR spectra
of compounds with their physical or chemical properties. In this chapter, some of the
essential knowledge for regressions analysis is presented, which will be used in the next
chapter for developing and assessing correlations.
3.2 Regression Analysis Methods
The performance of a regression method depends on the application, the availability
of data and the availability of knowledge regarding the final mathematical form of the
regression equation. In order to find the best methods to be used in our analysis, many of
the regression analysis methods available in commercial statistical software were applied
to the data sets developed for this project. Although the regression analysis could be
applied to data that have NMR spectra similar to the jet fuel (as has been done in
the case of diesel fuel [46]), data points outside those ranges were also included so that
the regression equations developed were general and could be used for different types of
compounds. This will help use these results in analyzing compounds and mixtures where
there are small shifts which are not found in a jet fuel. A drawback of this approach is
the larger root mean square error (RMSE) values.
17
Chapter 3. Regression Analysis Procedure 18
3.2.1 Multiple Linear Regression
Multiple linear regression (MLR) analysis was performed using different types of Ordinary
Least Squares (OLS) methods. The best results were obtained using the High Precision
OLS (HP OLS) algorithm implemented in the GRETL software package [47]. Hence,
this specific package was chosen for developing MLRs. Overall, MLR results were less
accurate compared to nonlinear models and are only reported for comparison.
3.2.2 Nonlinear Regression Analysis
Nonlinear Least Squares Method
The least squares solver minimizes the sum squared error, but requires the mathematical
form of the regression equation as an input. This solver was used on the data sets using
different mathematical forms. Polynomials were fitted to the data using RAPIDMINER
[48] and MATLAB’s curve fitting tool [49]. Custom models were also developed using
MATLAB based on the variation of the target property with different predictor param-
eters. Using the screening function in the JMP software package [50], models based on
complex predictors formed from mathematical manipulation of initial predictor param-
eters were developed and assessed. Due to the fact that the nonlinear equations had to
be supplied to the algorithm, the results did not achieve high enough R-squared values
when compared to other options such as ANNs (as outlined in the next section). Hence,
nonlinear least squares results will not be presented in this work.
Artificial Neural Network (ANN) Models
It has been suggested that when the nonlinear relationship between the target property
and regression parameters is not known, artificial neural networks are the best choice for
creating accurate regression models [51]. The ANN simply minimizes the mean squared
error by changing the internal parameters of the mathematical transfer function defined
for the neurons forming the artificial neural network. This internal transfer function can
be thought of as a transformation of the data. After fitting, the ANN’s internal transfer
function may be used as a regression equation.
The ANNs used for fitting are usually made of a hidden layer and an output layer. Several
functions can be used as the transfer function for the neurons. The standard ANN fitting
tool implemented in MATLAB uses a set of nonlinear neurons with a hyperbolic tangent
transfer function whose outputs are transformed by a linear transfer function to create
the final output of the network. In other words, the results will be a linear combination
Chapter 3. Regression Analysis Procedure 19
of several hyperbolic tangent functions. The algorithm finds values for the weights and
biases applied to the inputs of each neuron and the outputs of the hidden layer.
By default, the MATLAB ANN fitting algorithm breaks down the data set into three
distinct sets in a random manner. One set is the training set, which is used in developing
the regression equation. The two other sets, called the verification set and the test set
are used to check for over-fitting. ANNs are prone to over-fitting the data and using
separate parts of the data for verification and testing purposes helps reduce the chance
of overfitting occurring. Although there are other methods by which to break the data
set down into three separate sets, this random approach reduces the bias. In all cases ran
during this work, 80% of the data was used as the training set, 10% as the verification set
and 10% as the test set. The algorithm automatically outputs the R-value (correlation
coefficient) for the regression in each set. The best regressions reach higher R-values,
near 1. The approach chosen in this project was to check the R-value in the three sets so
that they were within comparable ranges of each other (usually ±0.1). The number of
hidden neurons was changed from 1 to the maximum possible and all regression results
that fitted this requirement were saved. The best regression was chosen from the set of
saved regression results based on comparison of total R-squared and RMSE values.
The number of coefficients in the model was calculated using:
ncoefficients = (npredictors + 3)nhidden + 1 (3.1)
In which ncoefficients is the number of coefficients in the model, npredictors is the number of
predictor parameters used and nhidden is the number of hidden neurons used in the model.
ncoefficients is important in assessing the model, as it should not exceed the number of
experimental data points available in the training set. The number of maximum hidden
neurons was calculated using equation 3.1 and the regressions were developed starting
with 1 hidden neuron and reaching the maximum number of hidden neurons. Due to
the random nature of breaking down the data set into three sets and the optimization
procedure, the results of consecutive regression analysis are different. The algorithm was
run many times (at least 20 times for each number of hidden neurons), so that the best
reliable results were achieved. The outputs of the regression analysis using the MATLAB
ANN fitting tool have the following mathematical form (using matrix notation):
f(Xk×1) = W1×n tanh(wn×kXk×1 + bn×1) +B (3.2)
Where k is the number of predictor parameters (inputs), n is the number of neurons
used by the ANN, w is the input layer weight, b is the input bias, W is the hidden
Chapter 3. Regression Analysis Procedure 20
layer weight and B is the hidden layer bias. The ANN fitting tool in MATLAB requires
the number of hidden neurons to be input by the operator. In the IBM SPSS package
[52], this parameter is automatically tuned. Moreover, this software package uses other
transfer functions such as hyperbolic sine for both the hidden and output layers. Using
different transfer functions (as tested with the software packages STATISTICA [53] and
IBM SPSS) proved no major improvements in the results compared to the MATLAB
standard model. As a result, only the results from the standard model in MATLAB are
reported in Chapter 4.
3.3 Regression Diagnostics
There are no generic criteria for assessing regression results as such criteria generally
depend on the specific algorithm. The main criteria for choosing regression models in
this work were the highest R2 value and the lowest Root Mean Square Error (RMSE).
Regression equations developed using ANNs might over fit the data, as mentioned earlier.
Although precautionary measures were taken to prevent this, there was no way to make
sure over fitting did not occur. Some of the diagnostic measures used in this project are
summarized in the next subsections. There are also many other statistical parameters for
assessing regression models; however, as such measures are not common among engineers,
they were not used in this work.
3.3.1 Coefficient of Determination (R2 Value)
This regression diagnostic parameter is mainly used in assessing least squares results as
they focus on minimizing the errors used in calculating this parameter. It can also be
used to compare results obtained using ANNs, but should be used with caution when
comparing different methods (linear models to artificial neural networks). As the R or
R2 increases towards one, the regression results become more reliable. However, there
is no specific threshold that marks an acceptable regression result. In most cases, an R
value of 0.9 and higher is considered acceptable for ANN analysis and an R2 value of
more than 0.9 for linear regression analysis. The results reported here have the highest
attainable R2 values. The R2 values attained are compared to values published in the
literature to ease assessing the regression results.
Chapter 3. Regression Analysis Procedure 21
3.3.2 Residuals
The least squares method requires that the residuals (difference between the predicted
values and actual values) form a normal distribution around zero. As a result, the average
of the residuals should be near zero and the standard deviation of the residuals should
be preferably within the error range of the experimental method. This requirement is
generally accepted for other regression methods as well. The histogram of the residuals
or a Normal Quartile Quartile plot (qqplot) can be used to check for normality.
The residuals should also be independent of the predicted and predictor values. To
check this, residuals can be plotted against the predictor, expected and predicted values.
The plot should show no special geometric feature. All the MLR results presented in
this report were checked for these requirements. For the ANNs, more than 50% of the
residuals were normal, the rest being at the lower range of the spectrum (helping reduce
the total RMSE value). As ANN regression does not require that residuals be normally
distributed, this aspect will not affect the result. In this case, only the mean and standard
deviations were checked.
3.3.3 Predicted Results
The mean and standard deviation of predicted values and the actual sample should be
the same. This is equivalent to the mean of the residuals being negligible. The plot of
predicted versus actual results was also used to assess the regression results, as it is the
best method of assessing the fitness of the regression model.
3.3.4 Root Mean Square Error
The root mean square error shows the general level of error seen when using a regression
equation. If the regression results met all other requirements, the most accurate regres-
sion model (the one with the lowest RMSE) was chosen. It should be noted that ANNs
all had lower RMSE values compared to their linear counterparts.
RMSE values depend on the units used. It is common practice to normalize these values
by the average experimental value of the parameter being predicted in the data set or
the difference between the maximum and minimum values in the data set. In this work,
normalization with respect to the latter will be used.
Chapter 4
Correlation Development for Fuel
Parameters
4.1 Chemical Structure and Nuclear Magnetic Res-
onance (NMR) Spectroscopy
4.1.1 Chemical Structure
Physical and chemical properties of a compound arise due to its chemical structure. Many
different parameters can be used to account for the chemical structure of a compound or
mixture, including:
• The type of atoms the molecule is made of and their relative numbers such as
carbon to hydrogen or oxygen to nitrogen ratios.
• Bonding and bond strength.
• Composition of mixtures as reported through mass percentage, volume percentage
or molar percentage.
Many methods have been used to quantify the chemical structure of compounds and mix-
tures. These include gas chromatography-mass spectrometry (GC-MS), nuclear magnetic
resonance (NMR) spectroscopy, liquid chromatography (LC) and infrared (IR) spec-
troscopy. Each of these methods reveals pieces of information about the chemical struc-
ture and environment of the compound or mixture. In this work, proton nuclear magnetic
resonance(NMR) spectroscopy is used as a measure of the chemical structure of the fuel.
This method reveals many details about the chemical structure and environment of a
22
Chapter 4. Correlation Development for Fuel Parameters 23
mixture. Moreover, facilities for measuring the NMR spectra of compounds are available
at the University of Toronto.
4.1.2 Nuclear Magnetic Resonance (NMR) Spectroscopy
One of the most powerful methods for predicting the structure of hydrocarbons is nuclear
magnetic resonance (NMR) spectroscopy [54]. NMR spectroscopy is based on the inher-
ent magnetic properties of the nucleus of different atoms. Magnetic nuclei are stimulated
by a magnetic field and their response in terms of the resonance frequency of the emitted
electromagnetic radiation is measured. Usually the frequency is Fourier transformed and
reported as a shift relative to a standard (tetramethylsilane (TMS) is usually assigned a
chemical shift of zero as the standard). A solvent is usually used in preparing mixtures
for the analysis and it slightly affects the chemical shifts observed. All isotopes that
contain an odd number of protons and neutrons have a nonzero spin and are possible
targets for NMR spectroscopy. In hydrocarbons, H-1 (proton) and C-13 can be used.
Specific ranges of chemical shifts have been correlated with specific functional groups in
chemical compounds. The spectrum output of NMR spectroscopy reveals the following
information about a compound:
• The different types of chemical environments present in the molecule as identified
by the different shift values.
• The relative numbers of the nuclei in each environment as identified by the area
under each shift.
• The electronic environment of the different types of nuclei as identified by the
location of the shift (up field or down field) in the shift range.
• The number of neighbors each nuclei has as identified by the splitting of the shifts.
4.1.3 Identifying Chemical Characteristics of Compounds and
Mixtures Using NMR Spectra
A Jet A sample from the combustion and propulsion group was analyzed by the NMR
services at the University of Toronto. The result of this analysis is depicted in Figure
4.1. The NMR test sample was prepared at the University of Toronto NMR facilities by
mixing equal parts of Jet A and CDCl3 (400 µL of each). The sample was placed in a 5
mm × 8 inch tube for one dimensional proton NMR acquisition using a Bruker Avance
Chapter 4. Correlation Development for Fuel Parameters 24
III 400 spectrometer. The spectrum was acquired at 25 ◦C over a 6410.3 Hz (16 ppm)
spectral window with a 1 s recycle delay.
0 1 2 3 4 5 6 7 8
0
4
8
12
16
In
tens
ity
(ppm)Figure 4.1: Complete proton NMR spectrum of the Jet A fuel from the combustion andpropulsion group. The horizontal axis shows the chemical shift and the vertical axis theintensity of each peak.
To use the information from the NMR spectrum, the spectrum was discretized into
several regions, each corresponding to a specific chemical environment. These regions
are summarized in Table 4.1. These proton NMR shift ranges were developed based
consensuses on the ranges of chemical shifts that correspond to different functional groups
[55, 56, 57, 58, 59, 60] and the Jet A NMR spectrum. In the following chapters, each
chemical range shift will be denoted using the letter “P” and a number corresponding
to the number assigned to each range in Table 4.1. It should be noted that, as most
CH3 shifts had a chemical shift less than 1 and most CH and CH2 shifts above 1, the
Chapter 4. Correlation Development for Fuel Parameters 25
general chemical shift group identified in most references as 0.5-1.6 was broken into two
categories. Moreover, this corresponded well to the two shifts seen in the Jet A NMR
spectrum between 0.5-1.6.
In breaking down the shift ranges, functional groups which are not found in the Jet A
were also taken into account. This was mainly due to the fact that databases used for
correlation development might have included compounds with similar shifts. Moreover,
although these groups are not found in aviation jet fuel, other functional groups can have
similar chemical shift values. It should also be noted that the NMR shift ranges outlined
in Table 4.1 are the most detailed version used in this work. Whenever possible, ranges
with similar group functionalities (overlapping functional groups) were lumped together
to simplify the regression analysis.
As mentioned earlier, the height of each shift shows the number of hydrogens contributing
to that shift. As a result, the area under two regions of the NMR spectrum can be used
to compare the relative number of protons in the two group functionality. As the area
under the curve is arbitrary, normalization of all area calculations will lead to values that
can be compared between different spectra.
AP1 + AP2 + AP3 + ...+ APn = 1 (4.1)
Where A denotes the area under the range of chemical shifts corresponding to the sub-
script, as outlines in Table 4.1. Values normalized in this way show the percentage of
protons in each range of chemical shifts, which can be used as a measure of chemical
composition.
Chapter 4. Correlation Development for Fuel Parameters 26
Table 4.1: Ranges of chemical shifts and their corresponding functional groups [55, 56,57, 58, 59, 60].
ProtonType No.
Min. Max. Proton Environments
1 0 1 Methyl (CH3), Tert-butyl ((CH3)3)2 1 1.6 Alkanes, CH2 , Amino (R − NH2)
3 1.6 2Allylic (CH2 = CHCH2), benzylic (C6H5CH2),Hydroxylic, amino (R − NH2), Alcohol, Amine
4 2 2.2
Benzylic (Ar-C-H), Acetylenic (C ≡ C − H), Esters(HC-COOR), Acids(HC-COOH), carbonyl compounds
(HC − C = O), iodides (HC-I), bromides (HC-Br),hydroxylic (ROH), amino (R − NH2)
5 2.2 2.7
Benzylic (Ar-C-H), Acetylenic (C ≡ C − H),Acids(HC-COOH), carbonyl compounds
(HC − C = O), iodides (HC-I), bromides (HC-Br),hydroxylic (R-OH), amino (R − NH2)
6 2.7 3Benzylic (Ar-C-H), Acetylenic (C ≡ C − H ), iodides(HC-I), bromides (HC-Br), hydroxylic (R-OH), amino
(R − NH2)
7 3 3.5Iodides (HC-I), bromides (HC-Br), chlorides(HC-Cl),
Ethers (HC-OR), hydroxylic (R-OH), amino (R − NH2)
8 3.5 4Alcohols (HC-OH), Ethers (HC-OR ), hydroxylic
(R-OH), amino (R − NH2)
9 4 4.5
Fluorides (HC-F), iodides (HC-I), bromides (HC-Br),chlorides(HC-Cl), hydroxylic (R-OH), Ethers
(HC-OR), Alcohols (HC-OH), esters(R-COO-CH),phenolic(Ar-OH), amino (R − NH2)
10 4.5 6Alkene, phenolic(Ar-OH), vinylic(C = C − H),
Aromatic (Ar-H), amino (R − NH2)
11 6 6.5Alkene, phenolic(Ar-OH), Aromatic (Ar-H), amino
(R − NH2)12 6.5 8.5 Aromatic (Ar-H)13 8.5 10.5 Aldehydic (R-CHO)14 10.5 13 Carboxylic (R-COOH)15 13 15 -16 15 17 Enolic (C = C − OH)
Chapter 4. Correlation Development for Fuel Parameters 27
4.2 Cetane Number (CN)
4.2.1 Ignition Quality and the Cetane Number
As mentioned in Chapter 1, ignition quality was chosen as one of the fuel properties
modeled using the surrogate fuel. Ignition quality is determined from the ignition pro-
cess. The injected fuel in an engine is first evaporated, leading to the physical delay in
ignition. Factors affecting evaporation include fuel properties (density, viscosity, surface
tension, specific heat, enthalpy of vaporization, vapor pressure, vapor diffusivity), air
properties (temperature, density, velocity and turbulence) and spray properties (atom-
ization, penetration and shape) [61]. For ignition to occur, the fuel should be heated so
that radicals form which can initiate the oxidation process. The rate of radical formation
is responsible for the chemical delay in ignition. Ignition will only be initiated when a
specific amount of radicals have formed.
The efficiency of the complete ignition process is quantified using the cetane number.
The cetane number (CN) is a measure of the ignition quality of diesel fuels. It is used
to quantify the ignition quality of middle distillates in diesel engines by measuring their
self-ignition delay, the time between injection and combustion [62]. It takes into account
all delay effects such as spray formation, heating, vaporization, mixing and chemical
induction times [63]. Of course, ignition delay is also dependant on engine type and op-
erating conditions. In the absence of a parameter to quantify ignition quality of jet fuel,
cetane number has been used extensively with jet fuels as a measure of ignition quality
due to the the similarities between jet and diesel fuels.
Cetane number is generally dependent on the chemical composition of the fuel and can
affect engine startability, noise level and exhaust emissions [64]. Fuels with low cetane
numbers generally lead to hard starting, tough operation, more noise and higher emis-
sions of particulate matter and NOx [65]. Particulate emissions is less affected by cetane
number compared to NOx formation [51, 66, 67, 68]. Cetane number has an inverse re-
lationship with octane number (ON), meaning a compound with a higher ON typically
has a lower CN [69].
The first proposed rating scheme for ignition quality was the cetene (ketene) rating.
Since cetene was hard to prepare, the higher reference value was later replaced with n-
hexadecane (cetane, hence the name change to cetane number) with a cetane number of
100. The lower reference was changed to 2,2,4,4,6,8,8- heptamethylnonane, assigned a
cetane number of 15. It has been suggested that cetane number of a mixture has a linear
relationship with the cetane number of its components, although this is not always true
[61].
Chapter 4. Correlation Development for Fuel Parameters 28
Empirical equations used for predicting cetane number are called cetane indices (CIs)
[70, 71, 72]. For convenience, most refineries rely on ASTM approved CIs which are
“non-engine” predictive equations for cetane number. Such indices are updated based on
the crude properties and composition. They generally relate to the mid-boiling point of
the fuel and the API gravity [54]. Many of the CIs can not be used with fuels contain-
ing cetane number improvers and are not applicable to vegetable oils, diesel fuel blends
containing alcohols, synthetic fuels derived from oil sands or oil shales [70].
The cetane number of a compound depends on its molecular structure [62]. Based on
experimental data, it has been deduced that normal alkanes have higher cetane numbers
than branched alkanes. Cyclo-alkanes and aromatics generally reduce cetane number,
unless they have an n-alkane group attached [63, 67]. A linear relationship between the
chain length and CN for compounds with 8-16 carbon atoms has been proposed for dif-
ferent classes of hydrocarbons [68, 73]. This shows that one of the primary factors in CN
determination is carbon chain length. Another suggested factor is the ratio of primary
to secondary C-H bonds in a molecule [73].
4.2.2 Cetane Number Measurement
The most accepted methods for measuring CN are the ASTM D613 (engine test) [74]
and the ASTM D6890 (IQT measurements) [75]. Overall, it has been suggested in the
literature that due to the simplicity of IQT tests and its higher accuracy and reproducibil-
ity, this test should replace the engine test. Unfortunately, only a few pure compounds
have been tested using the IQT procedure which reduces the usefulness of these data.
Of course, there have also been many alternative experimental methods developed for
measuring CN or ignition delay, such as the combustion bomb experiment [76]. Such
methods have not been widely used.
ASTM D613
ASTM D613 is the more prominent standard for CN measurement. It is based on the
measurement of the ignition delay in a standard CFR test engine built by the Waukesha
company [61]. Other standardization agencies have similar tests with engines manufac-
tured by the country of origin of the standard. This method has several limitations. It
requires a large volume of fuel sample of high purity (about 1 L), takes typically long to
test (approximately a few hours) and has a high reproducibility error (3-5 CN numbers)
[63, 61, 77] (Note that the ASTM standard cites a reproducibility error of 0.8 [78].).
Despite all its flaws, ASTM D613 measurements and test facilities are widely available.
Chapter 4. Correlation Development for Fuel Parameters 29
Ignition Quality Tester (IQT)
IQT is an alternative method developed by Southwest Research Institute (SwRI). It
requires a Constant Volume Combustion Apparatus (CVCA) which is developed by Ad-
vanced Engine Technology Ltd. This method measures the ignition delay which is corre-
lated with the cetane number. Details of this method are available in references [79, 80].
CN measured using this method is called the derived cetane cumber (DCN). IQT mea-
surements require a smaller sample volume (less than 50 mL [77], although 100 ml has
also been cited as the sample size [62].) and a much shorter time (less than 10 min).
This testing method operates based on the ASTM D6890 standard [75] and has a repro-
ductivity error of 1 to 2 cetane numbers [77]. It has been mainly used for measurements
of CN of middle distillates and alternative fuels. Despite the availability of test facilities,
reported values of IQT measurements are rare compared to the ASTM D613 method.
4.2.3 Sources of Cetane Number Data
In order to develop correlations between CN and fuel chemistry, a CN database was
developed. Most CN data for this database were acquired from reference [61]. These
data were measured or calculated using the following methods:
• Cetene rating.
As previously mentioned, cetene ratings had been used before the CN rating was
established. Cetene ratings can be transformed to CNs using a correlation [61].
• ASTM D613.
• Blend CN.
In some cases, measurements were not available for pure compounds and instead
blends of compounds with a specific composition were tested. In such cases, the
CN of the pure compound was wstimated from the blend cetane number. Such
data are of high uncertainty and are based on the assumption that the CN of the
blended mixture has a linear relationship with the CNs of its components. It is
suggested that large errors might exist for blend CNs [61].
• Cetane numbers based on ignition delay correlations.
These are cetane numbers which were calculated based on the ignition delay calcu-
lated for a special fuel using correlations developed between CN and ignition delay.
IQT measurements were considered separately, due to their higher accuracy and
reproducibility.
Chapter 4. Correlation Development for Fuel Parameters 30
• Derived CNs based on IQT measurement.
• CNs based on Octane Number correlations.
Various sources were used in the creation of the CN database [61, 62, 68, 69, 70, 81, 82,
83, 84, 85, 86, 87, 88]. There were a lot of overlap between data in these sources and
several issues existed with the numbers acquired including:
• In many cases, duplicate data did not agree. Fluctuations of 5 to 10 cetane num-
bers (and even higher) were noticed. When small fluctuations existed in the data,
average values were used.
• There was not enough information on the purity of the compounds used in the
measurements, specially in older sets of data.
• There is no standard for extending the Cetane Rating to below zero and over 100
[61].
• In some cases, the method used to measure CN was not stated by the source.
4.2.4 Correlations Development for Cetane Number
Correlations between the CN and other properties of fuels have been developed in order
to make CN prediction simpler. These correlations are either based on thermophysical
properties or the chemical structure of the fuel.
Physical properties are a good indicator of chemical structure for many hydrocarbon
compounds. As a result, they may be used for correlating a chemical phenomenon (igni-
tion) with a compound. Physical properties typically correlated with CN include aniline
point, density, mid-boiling point, viscosity, heat of vaporization and heat of combustion.
Density and aniline point are somehow indicators of the composition of the mixture,
while boiling point and viscosity are indicators of molecular size and mass [70].
Obviously, thermophysical properties stem from fuel chemistry. As a result, there has
been an increased interest in correlating different fuel characteristics directly with the
fuel chemical structure. It has been suggested that due to the changes in most cetane
indices, an index based on compositional analysis might be better predictor of CN com-
pared to indices based on physical properties [89]. This requires the characterization of
different classes of hydrocarbons available in the fuel. Different spectroscopic methods
may be used for such correlation development, creating a field called chemometrics [63].
Such models have been proposed based on NMR and IR spectra, liquid chromatography
Chapter 4. Correlation Development for Fuel Parameters 31
and gas chromatography-mass spectrometry (GC-MS) [51, 77]. They have reached ac-
ceptable results but extrapolation of these models is not reasonable since most of them
are based on linear assumptions and special functional forms. Moreover, such models
are application specific, focusing on special fuels and need to be updated. Another prob-
lem with such methods is that an overlap between the spectra of different hydrocarbon
species might exist which causes confusion in interpretation [89]. It should be noted that
analytical methods based on topological indices have also been used to develop prediction
models for cetane number [90, 91].
A review of quantitative structure-property relationships (QSPRs) for cetane number
shows that most CN QSPRs have an R2 value in the range 0.79 to 0.97 [92]. Reviewing
previous QSPRs developed for CN also reveals that as the range of CN values to which the
correlations is applicable increases, the R2 value decreases and the RMSE increases [93].
The statistical properties of some of the correlations developed for CN are summarized
in Table 4.2. As evident from this table, several simple linear and nonlinear correlations
for CN have been published with correlation coefficients of 0.9 to 0.99. However, in most
cases the correlation equations were solved and tested by the same data set which, with
a limited and insufficiently diverse data set, may lead to an overly optimistic assessment
of the correlation. Moreover, they mainly focus on special fuels or classes of compounds,
helping them achieve better regression statistics at the expense of generality. The R2
and RMSE values in Table 4.2 will be used as references in assessing the suitability of
CN correlations developed in this work.
4.2.5 Correlation of Cetane Number with NMR Spectrum
As previously mentioned, a database of CN data and NMR spectra of compounds was
created. Initial regression studies using all the CN data revealed that the difference in
experimental methods used to acquire the data created large errors for regression anal-
ysis. The best regression results were achieved when only the ASTM D613 data were
used. This was reasonable, since the ASTM D613 is the standard method of testing
and many of the pure compound properties were measured using this method. It should
also be noted that only hydrocarbons were used in regression analysis, since our focus
is on the aviation jet fuel which is primarily composed of carbon and hydrogen. The
properties of the data set used in the regression analysis along with the statistics of the
results obtained using high precision MLR and ANNs are summarized in Table 4.3.
All linear regression models met the requirements for the normality of residuals and their
independence from predicted and predictor values. They also had R2 values higher than
Chapter 4. Correlation Development for Fuel Parameters 32
Table 4.2: Statistical properties of some of the correlations proposed for CN (MLRdenotes Multiple Linear Regression, MNR denotes Multiple Nonlinear Regression andANN denotes Artificial Neural Network).
Predictor Range Data Set Size R2 RMSE Method Source1 Proton NMR 20-75 67 fuel mixtures diesel 0.992 1.11 MNR [94]
2 Proton NMR -10-100140 diesel fuels, pure
hydrocarbons andhydrocarbon blends
0.99 2.4 % MNR [46]
3 Proton NMR 48-55 (IQT) - 0.998 - MLR [95]4 Proton NMR 48-56 60 diesel fuels 0.97 (training) - MLR [63]5 Proton NMR 48-56 60 diesel fuels 0.91 (training) - ANN [63]6 Proton NMR + HPLC 43-64 53 diesel fuels and gas oils 0.692 2.11 MLR [89]7 C-13 NMR 13-57 93 hydrocarbon mixtures 0.98 2.0 - [78]8 C-13 NMR 40-71 21 diesel fuels 0.92 2.5 MLR [93]9 C-13 NMR 27.1-64.5 46 diesel fuels 0.95 2.8 MLR [93]10 C-13 NMR 31.2-68.4 46 diesel fuels 0.93 2.9 MLR [93]11 C-13 NMR 25.6-80.8 46 diesel fuels 0.94 4.1 MLR [93]8 C-13 NMR 37-72 81 diesel fuels 0.94 2.4 MLR [96]
8C-13 NMR and two points
on distillation curve37-72 81 diesel fuels 0.95 2.2 MLR [96]
12 C-13 NMR + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.92 2.7 MLR [97]13 C-13 NMR + HPLC 40-71 21 diesel fuels 0.92 2.4 MLR [93]14 C-13 NMR + HPLC 27.1-64.5 46 diesel fuels 0.95 2.8 MLR [93]15 C-13 NMR + HPLC 31.2-68.4 46 diesel fuels 0.94 2.8 MLR [93]16 C-13 NMR + HPLC 25.6-80.8 46 diesel fuels 0.95 4.1 MLR [93]17 GC + HPLC 31.2-68.4 (CI) 27 diesel fuels 0.88 3.5 MLR [97]18 LC and GC-MS 30.9-56.8 69 diesel fuels 0.94 - ANN [51]19 LC and GC-MS 30.9-56.8 69 diesel fuels 0.75 - MLR [51]
20 - 10-110paraffins, isoparaffins, and
cycloparaffins0.89 - ANN [98]
21 - -10-90 olefins and aromatics 0.89 - ANN [98]22 Topological indices 10-110 alkanes and cycloalkanes 0.99998 (training) - - [90, 91]23 Compositional lumps 20-60 (IQT) 203 diesel fuels - 1.25 - [77]24 Chemical Structure 10-90 isoparrafins 0.97 - ANN [99]
25 Molecular descriptors -hydrocarbons likely to be
present in deisel fuel0.886-0.978(training)
2-7.1 (training) MLR [62]
26 Aniline point 10-70 3400 diesel fuels 0.89 2.0 Functional Fitting [71]
27Distillation properties and
density10-70 1531 diesel fuels 0.9 1.9 Functional Fitting [71]
28Distillation properties,
density and aniline point10-70 - 0.92 1.7 Functional Fitting [71]
29 Physical properties 30.9-56.8 120 diesel fuels 0.86 1.62 ANN [99]
0.8. The actual values when plotted against predicted values , as illustrated in Figure
4.2, show that the linear models can have large errors in the range of CN of aviation jet
fuel (30-60). Moreover, normalized RMSE values are 9-10 %, which is higher than most
values cited in the literature.
To reach better regression results, artificial neural network (ANN) models were developed
for the CN data. These models all have R2 values higher than 0.9. RMSE values have
been approximately halved compared to the linear models and have reached values that
are near the experimental error of the ASTM D 613 standard which is less than 5 numbers
in CN [61]. Comparing the normalized RMSE values to those found in the literature,
we see that they are only slightly higher than those observed in Table 4.2. This can be
justified by the varying chemistry used in developing the correlations. The correlations
developed here cover a wider range of CN values, as this is required in analyzing mixtures
made from different chemical compounds. The results show a really good fit to available
Chapter 4. Correlation Development for Fuel Parameters 33
data in the region of CN = 30-60, which is the range of typical aviation jet fuel cetane
numbers.
Note that in both the MLR and ANN correlations, the importance of molecular mass
(MM) is apparent. The addition of molecular mass reduces the RMSE values dramat-
ically. This is physically acceptable, since ignition requires evaporation, which is de-
pendant on molecular mass. The fit acquired using different MLR and ANN models is
compared in Figure 4.2, plotting predicted values against actual values. It is apparent
that ANNs have better accuracy in predicting the cetane number. For the coefficients
and mathematical form of the regression results, please consult Appendix A.
The models developed in this work (MLR 1, MLR 4, ANN 1 and ANN 4 models) are
compared to several other models proposed for CN prediction in Figure 4.3. The ANN
models show comparable accuracy relative to the previous regression results develop and
seem to be acceptable tools for CN prediction.
Table 4.3: Statistical properties of the regression models developed for CN.
Properties of the data set used for regression analysisExperimental method ASTM D 613 Number of compounds 53
Atoms C, H Mean 46.96Range of values -20 to 110 Standard deviation (SD) 35.18
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.81 0.83 0.87 0.87
Adjusted R2 0.81 0.83 0.86 0.87RMSE 13.57 13.09 11.87 11.75
Normalized RMSE (%) 10.44 10.07 9.13 9.040Mean of Residuals -4.91E-07 -2.50E-06 1.69E-06 1.18E-06SD of Residuals 14.91 14.23 12.63 12.48
Range of Residuals -44.3 to 37.1 -30.2 to 34.8 -41 to 12.6 -40.7 to 28.8Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.94 0.94 0.95 0.96
Adjusted R2 0.94 0.94 0.95 0.96RMSE 8.70 7.96 7.84 6.60
Normalized RMSE (%) 6.70 6.12 6.03 5.08Mean of Residuals 0.77 1.21 0.72 -0.63SD of Residuals 8.63 8.83 7.99 6.72
Range of Residuals -25.8 to 18.7 -19.1 to 26.6 -18.9 to 28.9 -25.7 to 14.2Training Set R 0.98 0.97 0.97 0.98
Validation Set R 0.91 0.95 1.00 0.98Test Set R 0.99 0.98 0.97 0.98
Chapter 4. Correlation Development for Fuel Parameters 34
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(a) Predicted vs. actual values for MLR 1 and ANN 1.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(b) Predicted vs. actual values for MLR 2 and ANN 2.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(c) Predicted vs. actual values for MLR 3 and ANN 3.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d ce
tane
num
ber
Actual cetane number
(d) Predicted vs. actual values for MLR 4 and ANN 4.
Figure 4.2: Cetane number regression results.
-20 0 20 40 60 80 100 120
-20
0
20
40
60
80
100
120 Perfect fit Paraffins, Creton et al. 2010 [59] Naphtenes, Creton et al. 2010 [59] Aromatics, Creton et al. 2010 [59] Olefins, Creton et al. 2010 [59] Gulder et al. 1989 [44] MLR 1 MLR 4 ANN 1 ANN 4
Pred
icte
d ce
tane
num
ber
Actual cetane number
Figure 4.3: Cetane number regression results compared to several proposed correlations.
Chapter 4. Correlation Development for Fuel Parameters 35
4.3 Sooting Tendency
4.3.1 Introduction
Soot particles are carbon particulate matter formed during combustion. In the combus-
tion literature, distinctions are made between two types of soot. The first type is in-flame
soot which is measured within the combustor. Affecting combustor durability, in-flame
soot relates more directly to the chemical composition of the fuel. Soot particles that
stick to combustor walls affect the flow field, combustion properties and heat transfer
rates of the combustor, usually leading to higher maintenance costs. In jet engines, soot
can cause erosion, if it sticks to turbine blades and stators. Moreover, it could turn into
carbon deposits which clog filters and plug the holes in the combustor wall that supply
dilution air to the combustion subsection. This in turn can disrupt flow in the combus-
tion chamber [35, 100].
The second class of soot particles are exhaust soot emissions, soot particles that exit the
engine. Obviously, part of the soot formed in the combustor either stays there or oxidizes
on its way towards the exhaust. As a result, exhaust soot emissions are generally lower
than soot formed in the combustor. Soot represents a significant component of the par-
ticulate matter (PM) emitted by engines [101]. PM emissions from soot have been linked
to lung and heart disease and cancer [102, 103, 104, 105, 106]. In addition, PM emissions
contribute to smog and reduced visibility, affect local climate, and play a significant role
in the global climate [107, 108, 109, 110]. Soot formation increases the exhaust emissions
of aircraft engines, an important factor in a military aircraft’s stealth capabilities. They
also reduce visibility on the ground when large quantities are formed by ground vehi-
cles [111]. Soot is also the main contributor to fire radiation [112, 113, 114, 115, 116].
Furthermore, soot is involved in the formation of the most common fire toxicant, carbon
monoxide [117, 118].
Due to all these detrimental effects of soot on human health and the environment, we
chose sooting tendency of aviation jet fuel as one of the properties the surrogate fuel has
to mimic. This will enable future researchers to conduct more detailed analysis on soot
formation using such surrogate fuels.
4.3.2 Effect of Chemical Structure on Sooting Tendency
It has been revealed that the fuel molecular structure has a significant effect on its sooting
tendency [119, 120, 121, 122]. Sooting has been correlated with the chemical structure
of the fuel [123, 124, 125, 126, 127, 128] alongside other fuel properties [123, 129]. There
Chapter 4. Correlation Development for Fuel Parameters 36
is still controversy on the effect of different functional groups on sooting tendency and
different sources have proposed different trends. Some sources cite the following general
trend between the sooting tendency of different classes of hydrocarbons of same chain
length in both laminar and diffusion flames [130, 131]:
acetylene < alkenes < isoalkanes < n-alkanes < mono-cyclic aromatics < naphthalenes
For laminar premixed flames, the following trend has also been suggested [132]:
Aromatics > Alkanes > Alkenes > Alkynes
While for laminar diffusion flames, the trend changes as follows [132]:
Aromatics > Alkynes > Alkenes > Alkanes
Note that the tendency to soot for alkanes and alkenes is reversed between the two
flames. In general, the tendency to soot increases with increasing molecular mass (in-
creasing number of carbon atoms) and isomerization (increasing molecular compactness
or branching) in both flames [126, 133, 134]. Higher aromatic content and lower hydrogen
content also correspond to increased soot and deposit forming tendency [135].
The following chemical structure based parameters have been used as predictor parame-
ters for correlation development for sooting tendency:
• Hydrogen content (H/C).
This parameter shows the share of hydrogens in the molecule and may also be used
to check the degree of saturation of the molecule. It was one of the early parameters
correlated with soot formation [136]. Generally, higher hydrogen content has been
correlated with lower soot formation [123]. Reduced hydrogen content is usually
due to the increased presence of aromatic hydrocarbons which are known as very
effective soot producers [135]. Some suggest that the increase in tendency to soot
with decreasing H/C ratio is a weak trend and thus of limited predictive value
[126]. Others have suggested that hydrogen content represents the effect of flame
temperature in soot formation [122].
• Aromatic content.
Aromatic compounds are generally more sooting than non aromatics [137]. As
a result, the higher the share of aromatics in a mixture, the more it will soot.
Distinction may also be made between mono-, di- and poly-cyclic aromatics. It has
been shown that the addition of a small amount of a very sooty (e.g. aromatic)
fuel to a less sooty fuel (e.g. alkane) results in a disproportionately large increase
in the sooting tendency of the fuel blend [138].
Chapter 4. Correlation Development for Fuel Parameters 37
• Cycloalkane content.
Results from analyzing smoking tendency (inverse of the smoke point) showed that
the tendency to smoke is directly proportional to cycloalkane content of a fuel [137].
Obviously, other parameters such as environmental conditions (pressure and tempera-
ture) also affect the formation of soot. Such effects are beyond the scope of this work.
4.3.3 Sooting Tendency Indices
There are many indices available for quantifying the sooting tendency of fuel mixtures,
for some of which mixture rules have also been developed. In this section, some of these
indices are reviewed.
Smoke Point (SP) and Sooting Height
Sooting height and smoke point have been used for many years in the automotive and
aerospace industries as a measure of the sooting tendency of diesel fuels. The ASTM
D1322 [139] is the standard used for most measurements. The higher the smoke point,
the lower the sooting tendency of the fuel. A problem associated with smoke point is the
operator dependence of its measurement. In the smoke point measurement, the observer
has to decide when the flame is at the smoke point and where its tip is located by visual
observation [140]. Moreover, smoke point is difficult to measure precisely for heavily
sooting hydrocarbons such as aromatics. In recent years, digital automated systems have
been developed for smoke point measurement which have higher degrees of accuracy.
Many sources of data are available for smoke point measurements [110, 125, 128, 141].
The standard ASTM smoke point lamp, which is especially designed for application to
aviation jet fuels, had not been developed at the time some of these measurements were
made. Moreover, this apparatus cannot measure a smoke point higher than 50 mm,
which is below the smoke point of most paraffinic compounds. These two issues affect
the suitability of SP data for use in this work.
It is generally recognized that substances with lower smoke points are in some sense
“sootier” than those with higher smoke points. The parameter “tendency to smoke” was
defined as a constant divided by the smoke point to explain sooting tendency [137].
Threshold Fuel/Oxidizer Ratios (Φc, Ψc and Sc)
Threshold fuel/oxidizer ratios were developed as indices for comparing sooting tendency
in premixed flames. They assume combustion to specific products (Φc assumes products
Chapter 4. Correlation Development for Fuel Parameters 38
of CO2 and H2O, Ψc assumes CO and H2O and Sc assumes C and H2O) [124, 127, 142].
The lower the carbon-to-oxygen ratio (C/O) or the critical equivalence ratio Ψc are, the
greater the tendency of the fuel to soot in a premixed flame [126].
Maximum Soot Volume Fraction or Mass Flow Rate at Sooting
Measured soot volume fractions (volumetric ratio of soot in a flame) and mass flow rates
at the onset of sooting in diffusion flames can be used as measures of sooting tendency if
the same experimental setting is used [125].
Threshold Soot Index (TSI)
Threshold soot index (TSI) was developed by combining several fuel parameters into a
single index. The aim of developing the TSI was “to define a parameter which reflects
the correlation of incipient sooting with molecular structure, i.e., the oxidative chemistry
of the fuel, and does not reflect differences in transport properties due to the nature of
the measurement apparatus or the quantity of oxygen which must diffuse into the flame
front (in the case of diffusion flames)” [126]. For premixed flames, the TSI is defined as
[126]:
TSI = a− bΦc (4.2)
Where a and b are device dependant constants and Φc is the threshold fuel/oxidizer ratio
which assumes complete combustion of the fuel to CO2 and H2O. For diffusion flames,
the TSI definition changes to [126]:
TSI = aMM
SP− b (4.3)
Where a and b are device dependant constants, MM is the molecular mass of the fuel
and SP is the smoke point of the fuel. As mentioned earlier, the reciprocal of the
smoke point was suggested as a sooting tendency index in diffusion flames [137]. The
introduction of fuel molecular mass is done to offset the minor flame height increase
caused by the increased fuel molecular mass, which requires a larger air/fuel volume
ratio for stoichiometric combustion [126].
Alternatively, the critical volumetric flow rate at which soot production is initiated in a
flame, V, may also be used as a measure of the tendency to soot in diffusion flames.
TSI = aMM
V− b (4.4)
Chapter 4. Correlation Development for Fuel Parameters 39
As a result of using the constants a and b, TSI values are hardware independent. The
TSI ratings of ethane and methyl naphthalene were assigned to be 0 and 100, respectively
and the a and b values were calculated based on this convention for each experimental
setting.
The significance of the TSI concept is that a numerical scale is established for the sooting
tendency of pure hydrocarbons. Since the constants a and b offset the effect of the test-
ing apparatus on measurement, TSI is device-independent and inherently determined by
hydrocarbon molecular structures, similar in principle to the octane and cetane ratings.
Special trends have been observed in the TSI of different chemical species. Both alka-
nes and alkenes have low sooting tendencies with their TSIs normally being less than
7, but alkenes have TSIs which are 2-6 units greater than those of alkanes with the
same number of carbons [134]. Aromatics have substantially higher TSIs than n-, iso-
and cyclo-alkanes. Naphthalenes have much higher TSIs than alkylbenzenes. Except for
alkane and alkene molecules, TSI of other compounds increases with increasing carbon
number [134]. In general, aromatic character greatly increases the tendency to form soot.
The TSI scale is said to have some limitations with respect to aromatics and, thus, other
indices have been proposed for aromatic compounds. TSI-structure relationships do not
fit many of the measured aromatic TSIs, which the authors of these relationships at-
tribute to errors in measurements [125, 134, 143]. Most TSI data have an uncertainty of
7% [125] to 15% [141].
Both definitions for the TSI (for premixed and diffusion flames) were used in creating
the database for this work using measurements presented in several different sources
[124, 125, 126]. There is scatter in some of the TSI data. Recommended averages were
used when available [125].
A limitation of the TSI model is that its value cannot be determined strictly by exper-
iment or theory. The TSIs of pure hydrocarbons were determined by normalizing and
averaging early smoke point results, which is the main source of uncertainty in the calcu-
lation of TSIs. The TSIs of mixtures are based on mixing rules, in which the coefficients
a and b require a large fuel database in order for their values to be determined with
sufficient accuracy [123]. The error limits for the experimental diffusion flame TSI data
are 10 percent of the TSI value. For small smoke points (10 mm), the error is due to
inaccuracy in reading the scale of the smoke point apparatus to better than 0.5. For
larger smoke points, the error (2-3 mm) arises due to uncertainty in determining when
smoke first escapes from the flame tip [138].
TSI mixture rules have been proposed for both types of flames and tested on binary and
Chapter 4. Correlation Development for Fuel Parameters 40
tertiary mixtures [138]. For premixed flames, the best rule is:
1.1TSImix = Σ1.1TSIiXi (4.5)
In which TSImix is the mixture TSI, TSIi is the TSI of the ith mixture component and
Xi is the molar fraction of the ith mixture component. A good fit was obtained using
this rule for binary and tertiary mixtures with a TSI of 35-56. For Diffusion flames:
TSImix = ΣXiTSIi (4.6)
These mixture rules were shown to hold over a wide range of mixture samples and be
applicable to complex mixtures such as aviation jet fuel [123]. There is usually little
difference between using mole fractions or volume fractions for most hydrocarbon blends
since the densities of most liquid hydrocarbons used in such blends are similar [138].
Yield soot index (YSI)
The YSI was proposed to assess the sooting tendency of aromatic compounds [140, 144].
It is defined as:
YSI = Cfvmax +D (4.7)
In which C and D are apparatus dependent constants and fvmax is the maximum soot
volume fraction measured in a co-flow methane/air non-premixed flame, whose fuel is
doped with 400 ppm of the hydrocarbon sample. YSI is scaled so that YSI-benzene =
30 (= TSI-benzene ) and YSI-1,2-dihydronaphthalene = 100. For most hydrocarbons,
YSI and TSI are equivalent methods for sooting tendency measurements (in fact, it has
been shown that there is a linear correlation between them [140]); however, the uncer-
tainty in measuring YSIs is lower (3% - 10%). The authors proposing the YSI argue
that YSI indicates the sooting tendencies of aromatics in the chemical environment of
an alkane-fueled flame, which represents a more realistic model for real fuels. Moreover,
YSI is more accurate than TSI because maximum soot volume fraction can be measured
more accurately than the smoke point for high sooting fuels (i.e., those high in aromatic
content). YSI measurements require smaller sample sizes and they measures the intrin-
sic sooting tendency of the additives without interference from indirect effects, such as
chemical reactions and changes in residence times, because the concentrations of aromatic
dopants are less than 400 ppm.
Chapter 4. Correlation Development for Fuel Parameters 41
Micro Pyrolysis Index (MPI)
The MPI is defined as the amount of carbon deposited from injection of 20 µL of a
sample, normalized to two reference compounds [145]. As a result, it does not take into
account the oxidation of soot particles which can affect the total amount of soot formed.
Only 13 data points were available for this index. A linear relationship exists between
the MPI and the TSI. It is suggested that there might be some problems with respect to
using this scale for aromatics. MPI was found to be more differentiating than TSI among
the different hydrocarbon families (n-alkanes, iso-alkanes, and cyclo-alkanes) [145].
4.3.4 Correlations Developed for Sooting Tendency
Sooting tendency has been correlated, as previously mentioned, with the chemical compo-
sition and structure of fuels and also thermophysical properties. The statistical properties
of some of these correlations are summarized in Table 4.4. As it is evident from this ta-
ble, smoke point correlations have achieved R2 values of 0.87-0.94 and RMSE values of
1.6-2.8, while TSI correlations have achieved R2 values of 0.94-0.99 and RMSE values of
2.4-8.5. These R2 and RMSE values will be used in the following section to assess the
correlations developed in this work.
Table 4.4: Correlations proposed for sooting tendency indices (MLR denotes multiplelinear regression and MNR denotes multiple nonlinear regression).
Predictor Parameter Range Data Set Size R2 RMSE Method SourceSmoke Point
1 C-13 NMR 7-38 56 kerosene 0.88 2.8 MLR [146]2 C-13 NMR 15-38 44 aviation jet fuels 0.87 2.2 MLR [147]3 C-13 NMR 15-43 72 aviation jet fuels 0.92 1.9 MLR [96]4 GC 7-38 39 kerosene 0.88 2.6 MLR [146]5 GC + HPLC 15-38 35 kerosene 0.91 1.9 MLR [146]6 C-13 NMR + HPLC 15-38 35 kerosene 0.88 2.1 MLR [146]
7C-13 NMR and 2 points
on distillation curve15-43 72 jet fuels 0.94 1.6 MLR [96]
TSI1 Topological Indices 4.5-100 93 pure compounds 0.945 5.7 MLR [134]2 Topological Indices 4.5-100 98 pure compounds 0.974 8.5 MNR [134]3 Structural Groups 0-100 - 0.9896 3.08 MNR [143]4 Structural Groups 0-100 - 0.9890 2.76 MNR [143]5 Structural Groups 0-100 - 0.9937 2.37 MNR [143]
Chapter 4. Correlation Development for Fuel Parameters 42
4.3.5 Correlation Development Between Sooting Tendency and
Proton NMR Spectra
Due to the non-premixed nature of jet engine combustor flames, this work will only focus
on sooting tendency parameters in diffusion flames. Correlations were developed between
fuel chemistry and smoke point, TSI and YSI. Due to the fact that YSI data are only
applicable to aromatic compounds, these results were removed. Since the TSI and YSI
scales are equivalent, another approach would have been to use them together; however,
an attempt at this lead to low correlation coefficients which were deemed unacceptable
for the purposes of this work.
Smoke Point Correlations
Table 4.5 summarizes the properties of the smoke point data set along with the re-
sults of the regression analysis. A notable characteristic of this data set was that many
compounds had the same smoke point, making it hard for the regression algorithm to
distinguish between these points. The values predicted using these correlations are plot-
ted against actual values in Figure4.4. The fact that different compounds had the same
smoke point is evident in the figure, as a straight line is formed near an actual smoke
point of 5. The mathematical form of the regression results can be found in Appendix
A.
Initially, linear methods were used for regression analysis. MLR results did not reach
acceptable fits. In fact, MLR correlations are not reliable for compounds with smoke
points less than 10, as their results lead to negative smoke points which are physically
impossible.
To increase the accuracy of the regression models, ANN models were used which achieved
acceptable fits with R2 values higher than 0.9 and lower RMSE values. The higher RMSE
values compared to cited models in the literature can be justified by the more diverse
chemistry of the data set. These models show acceptable accuracy around smoke points
of 20-25. As outlined in Chapter 3, this is the typical range of smoke points of aviation
jet fuels.
Chapter 4. Correlation Development for Fuel Parameters 43
Table 4.5: Statistical properties of the regression models developed for smoke point.
Properties of the data set used for regression analysisExperimental method ASTM D1322 Number of Compounds 74
Atoms C, H Range of values 4-149Mean 56.39 Standard deviation (SD) 49.55
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.75 0.81 0.77 0.82
Adjusted R2 0.75 0.81 0.76 0.82RMSE 21.51 19.64 21.10 19.12
Normalized RMSE (%) 14.83 13.54 14.55 13.18Mean of Residuals -3.10E-06 5.12E-06 1.99E-06 6.24E-07SD of Residuals 24.61 21.69 23.93 20.95
Range of Residuals -81 to 78.1 -71.6 to 56.8 -76 to 68.1 -66.7 to 53.2Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.93 0.97 0.95 0.96
Adjusted R2 0.93 0.96 0.95 0.96RMSE 12.97 9.15 10.75 9.75
Normalized RMSE (%) 8.94 6.31 7.41 6.72Mean of Residuals 0.15 0.32 1.40 -0.06SD of Residuals 13.12 9.23 10.83 9.87
Range of Residuals -36.3 to 35.7 -24.4 to 31.9 -33.9 to 34.2 -40.6 to 30Training Set R 0.97 0.98 0.98 0.98
Validation Set R 0.95 0.97 0.96 0.99Test Set R 0.95 1.00 0.9706 1.00
-20 0 20 40 60 80 100 120 140 160 180-20
0
20
40
60
80
100
120
140
160
180 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d sm
oke
poin
t, m
m
Actual smoke point, mm
(a) Predicted vs. actual value for MLR 1 and ANN 1.
-40 -20 0 20 40 60 80 100 120 140 160 180-40
-20
0
20
40
60
80
100
120
140
160
180 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d sm
oke
poin
t, m
m
Actual smoke point, mm
(b) Predicted vs. actual value for MLR 2 and ANN 2.
Figure 4.4: Regression analysis results for smoke point.
Chapter 4. Correlation Development for Fuel Parameters 44
-60 -40 -20 0 20 40 60 80 100 120 140 160 180-60
-40
-20
0
20
40
60
80
100
120
140
160
180 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d sm
oke
poin
t, m
m
Actual smoke point, mm
(c) Predicted vs. actual value for MLR 3 and ANN 3.
-40 -20 0 20 40 60 80 100 120 140 160-40
-20
0
20
40
60
80
100
120
140
160 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d sm
oke
poin
t, m
m
Actual smoke point, mm
(d) Predicted vs. actual value for MLR 4 and ANN 4.
Figure 4.4 (continued): Regression analysis results for smoke point.
TSI Correlations
Table 4.6 summarizes the properties of the TSI data set used in the regression analysis
and the results of this analysis. The TSI data were all based on diffusion flames. Many
of the data points used in the analysis came from the work of Olson et al. [125] who had
standardized the TSI values for some of the compounds based on their own experiments.
Initially, MLR was used in the analysis. By adding parameters such as molecular mass
and H/C, the regression results became more accurate with lower RMSE values. The
accuracy of these models are low and errors can be large in some cases, as revealed by
Figure 4.5 which depicts predicted values against actual values.
To increase the accuracy of the regression results, artificial neural network models were
developed for the threshold sooting index data. As it is apparent from the plots in Figure
4.5, the fit remarkably improved in these models, with the best fit being attained using
NMR, H/C and MM. The statistics in terms of R2 and RMSE values improved, with
RMSE values matching some of the correlations previously proposed in the literature.
The regression results fit the experimental data well in the range 15-30, which is typical
of jet fuels. Comparison of these results with two of the correlations proposed in the
literature by Hanson et al. [134] as illustrated in Figure 4.6 shows that the models
developed here are of comparable accuracy. For the mathematical form of the regression
results presented in this section, please consult Appendix A.
Chapter 4. Correlation Development for Fuel Parameters 45
Table 4.6: Statistical properties of the regression models developed for TSI.
Properties of the data set used for regression analysisExperimental method - Number of compounds 91
Atoms C, H Range of values -0.2 to 100Mean 22.71 Standard deviation (SD) 27.10
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.78 0.81 0.80 0.82
Adjusted R2 0.78 0.80 0.80 0.82RMSE 11.23 10.80 10.94 10.51
Normalized RMSE (%) 11.21 10.77 10.92 10.49Mean of Residuals -2.50E-06 8.77E-07 -1E-06 7.95E-07SD of Residuals 12.62 11.96 12.18 11.55
Range of Residuals -45.6 to 65.8 -47.8 to 66.5 -40.3 to 63.8 -42.7 to 64.5Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.87 0.88 0.91 0.91
Adjusted R2 0.87 0.88 0.90 0.90RMSE 9.23 8.95 7.82 8.13
Normalized RMSE (%) 9.21 8.94 7.81 8.12Mean of Residuals 0.32 -0.34 0.23 -1.10SD of Residuals 9.72 9.40 8.35 8.33
Range of Residuals -35.9 to 63.1 -34.5 to 62.9 -25.5 to 40.4 -23.4 to 50.0Training Set R 0.93 0.94 0.95 0.95
Validation Set R 0.99 0.98 0.98 0.98Test Set R 0.95 0.96 0.96 0.93
0 20 40 60 80 100
0
20
40
60
80
100 Perfect fit MLR 1 ANN 1 training set aNN 1 validation set ANN 1 testing set
Pred
icte
d TS
I
Actual TSI
(a) Predicted vs. actual value for MLR 1 and ANN 1.
-20 0 20 40 60 80 100-20
0
20
40
60
80
100 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d TS
I
Actual TSI
(b) Predicted vs. actual value fpr MLR 2 and ANN 2.
Figure 4.5: Diffusion flame TSI regression analysis results.
Chapter 4. Correlation Development for Fuel Parameters 46
0 20 40 60 80 100
0
20
40
60
80
100 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d TS
I
Actual TSI
(c) Predicted vs. actual value for MLR 3 and ANN 3.
-20 0 20 40 60 80 100-20
0
20
40
60
80
100 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d TS
I
Actual TSI
(d) Predicted vs. actual value for MLR 4 and ANN 4.
Figure 4.5 (continued): Diffusion flame TSI regression analysis results.
-20 0 20 40 60 80 100-20
0
20
40
60
80
100 Perfect fit Hanson et al. 1987 [132] Hanson et al. 1987 [132] MLR 3 MLR 4 ANN 1 ANN 4
Pred
icte
d TS
I
Actual TSI
Figure 4.6: Comparison of diffusion flame TSI regression results to correlations proposedin the literature.
Chapter 4. Correlation Development for Fuel Parameters 47
4.4 Thermophysical Properties
4.4.1 Introduction
Thermophysical properties affect the flow field inside a propulsion system and other pro-
cesses such as mixing and evaporation. Boiling point, freezing point, density and viscosity
were identified in Chapter 1 as target parameters for the surrogate fuel being developed
in this work. Molecular mass was also included as an auxiliary parameter in the regres-
sion analysis. A database of boiling point, freezing point, density and viscosity values
was created using data from references [44, 148].
Density affects the flow field, atomization and mixing in the combustion chamber. It is
also one of the thermophysical parameters regulated by fuel specifications. It should be
noted that density is known to be less sensitive to fuel composition compared to other
thermophysical properties [18]. Quantitative structure-property relationships (QSPRs)
developed for density typically have R2 values in the range of 0.815 to 0.984 [92].
Boiling point (BP) and freezing point (FP) mark temperatures at which phase changes
occur. Boiling point was included as a measure of volatility of the fuel, which affects
pre-combustion processes in the combustion chamber [14] and provides valuable insight
into the performance of engines. Aviation jet fuel specifications specify the final boiling
point and the maximum freezing point of the fuel. Whenever used in this work, Boiling
point will correspond to the initial boiling point of a mixture (and normal boiling point
of a compound) and freezing point will correspond to the maximum freezing point. A
review of different QSPRs developed for boiling point showed that the typical R2 values
are 0.954 to 0.998 with standard deviation of residuals being 0.97 to 11.6 [92].
Viscosity affects pre-combustion processes in combustion chambers with short residence
times and high efficiency requirements [1, 14]. Viscosity is highly sensitive to both chemi-
cal composition and temperature [3] and is regulated by fuel specifications. For viscosity,
QSPRs have R2 values in the range of 0.854 to 0.908 [92].
Table 4.7 summarizes some of the correlations developed between chemical structure of
the fuel and boiling point, freezing point, density and dynamic viscosity along with their
statistical properties. It is evident that multiple linear regression and artificial neural
network models have both been previously used in developing regression equations for
these properties.
Chapter 4. Correlation Development for Fuel Parameters 48
Table 4.7: List of some of the QSPRs proposed for thermophysical properties of interest.
Predictor Parameter Range Data Set Size R2 RMSE Method SourceBoiling Point (K)
1Semi-empirical
quantum-chemicaldescriptors
200-580 59 hydrocarbons 0.986-0.997 5.4-10 ANN [149]
2 Wiener indices 260-40037-39 straight-chain andbranched-chain alkanes
C2-C80.977-0.992 2.37-7.59 MLR [150]
3 Wiener indices 330-500 37 aliphatic alcohols 0.913-0.993 1.44-10.3 MLR [150]
4 Topological indices 115-450327 aliphatic hydrocarbons
C1-C100.9933-0.9999 0.8-4.46 ANN [151]
5 Structural graphs 330-440 134 hydrocarbons C6-C10 -1.3-2.7 % training
2% testingANN [152]
6 Structural graphs 330-443 134 alkanes C6-C10 0.990 - ANN [153]
7Atom type
electrotopological stateindices
225-650298 heterogeneous set of
organic compounds- 1.17 % ANN [154]
8Topological, geometrical,
and electronicdescriptors
225-648 298 organic compounds 0.988 2.7 % ANN [155]
Maximum Freezing Point (K)1 C-13 NMR 223-241 25 kerosene fuel 0.76 2.2 MLR [146]2 C-13 NMR 200-240 47 aviation jet fuels 0.59 5.8 MLR [96]3 C-13 NMR 200-240 47 aviation jet fuels 0.93 2.5 MLR [96]4 C-13 NMR + HPLC 223-241 25 kerosene fuels 0.76 2.1 MLR [146]5 GC 223-241 25 kerosene fuels 0.91 1.3 MLR [146]6 GC 223-241 25 kerosene fuels 0.96 0.9 MLR [146]7 GC + HPLC 223-241 25 kerosene fuels 0.92 1.2 MLR [146]
Density (kg/m3)1 Proton NMR 0.8233-0.8455 60 diesel samples 0.998 1.11 MLR [95]2 C-13 NMR 0.765-0.871 72 aviation jet fuels 0.82 0.011 MLR [96]3 C-13 NMR 0.803-0.909 81 diesel fuels 0.88 0.011 MLR [96]
4C-13 NMR + two points
on distillation curve0.765-0.871 72 jet fuels 0.91 0.008 MLR [96]
5C-13 NMR + two points
on distillation curve0.803-0.909 81 diesel fuels 0.92 0.008 MLR [96]
6 GC-MS + LC 0.83-0.89 69 diesel fuels 0.96 0.003 ANN and MLR [51]
7 Structural graphs 0.65-0.76 134 hydrocarbons C6-C10 -1.3-2.7 % training
2% testingANN [152]
Dynamic Viscosity (mm2/s)1 Proton NMR 2.15-3.15 60 diesel samples 0.998 0.09 MLR [95]
4.4.2 Density Correlations
Table 4.8 summarizes the properties of the density dataset used in this work along with
the best results attained in the regression analysis. All densities were evaluated at 298.15
K.
Initially, MLR was used to develop correlations between density and the predictor pa-
rameters. These regressions possess the required accuracy for densities in the range of
0.7-0.9 kg/L, which is similar to the density of jet fuels. This accuracy is evident in
Figure 4.7. Despite this accuracy, the MLR regressions can have large errors in many
cases and are not reliable.
To increase the reliability of the regressions, ANN models were developed. These models
achieved lower RMSE values and seem to better fit the experimental data. When molec-
Chapter 4. Correlation Development for Fuel Parameters 49
ular mass is included as a predictor parameter, the ANN correlations seem to reach a
perfect fit. It should be noted that a point with a density of 2 kg/m3 existed in the data
set. Since ANN 2 and ANN 4 match this value perfectly, this point was retained in the
data set to increase the range of applicability of the regressions.The mathematical form
of all results is available in Appendix A.
Table 4.8: Statistical properties of the regression models developed for density.
Properties of the data set used for regression analysisUnit kg/L Number of compounds 148
Atoms C, H Range of values 0.31-1.98Mean 0.79 Standard deviation (SD) 0.16
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.53 0.62 0.63 0.63
Adjusted R2 0.53 0.62 0.63 0.62RMSE 0.08 0.08 0.08 0.08
Normalized RMSE (%) 4.76 4.64 4.60 4.62Mean of Residuals 7.76E-09 7.91E-09 -6.4E-09 2.82E-09SD of Residuals 0.11 0.10 0.10 0.10
Range of Residuals -0.33 to 0.97 -0.49 to 0.86 -47 to 0.9 -0.47 to 0.9Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.70 0.99 0.88 1.00
Adjusted R2 0.69 0.99 0.88 1.00RMSE 0.08 0.02 0.05 0.01
Normalized RMSE (%) 4.54 0.99 3.00 0.66Mean of Residuals 2.33E-3 8.88E-4 4.121E-3 1.07E-3SD of Residuals 0.09 0.02 0.05 0.01
Range of Residuals -0.4 to 0.7 -0.03 to 0.04 -0.4 to 0.4 -0.04 to 0.04Training Set R 0.83 1.00 0.94 1.00
Validation Set R 0.88 0.93 0.97 0.99Test Set R 0.94 0.99 0.96 0.99
Chapter 4. Correlation Development for Fuel Parameters 50
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
1.5
2.0 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d de
nsity
, kg/
m3
Actual density, kg/m3
(a) Predicted vs. actual value for MLR 1 and ANN 1.
0.0 0.5 1.0 1.5 2.00
1
2 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d de
nsity
, kg/
m3
Actual density, kg/m3
(b) Predicted vs. actual value for MLR 2 and ANN 2.
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
1.5
2.0 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d de
nsity
, kg/
m3
Actual density, kg/m3
(c) Predicted vs. actual value for MLR 3 and ANN 3.
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
1.5
2.0
Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d de
nsity
, kg/
m3
Actual density, kg/m3
(d) Predicted vs. actual value MLR 4 and ANN 4.
Figure 4.7: Density regression results.
4.4.3 Boiling Point Correlations
Table 4.9 summarizes the properties of the boiling point data set used in the regression
analysis along with the statistics of the regression results obtained. All data used in
developing the regression were normal boiling point values. The mathematical form of
the regression results can be found in Appendix A. It was possible to focus the regression
analysis to the range of boiling point values found in jet fuel; however, this was not done
due to the diversity of chemical compounds used later in the mixture analysis.
The MLR analysis did not yield low enough RMSE values. They only achieved acceptable
accuracy when molecular mass is included as a predictor parameter in the regression
analysis. The ANN models achieved high R2 and low RMSE values that are comparable
Chapter 4. Correlation Development for Fuel Parameters 51
to results reported in the literature. The regression results are also illustrated in Figure
4.8, which clearly shows the higher accuracy of the ANN results. It is evident from the
results that molecular mass is an important predictor parameter for boiling point. Figure
4.9 compares ANN 4 to several correlations proposed in the literature. This reveals that
the model developed in this work has accuracy comparable to other models proposed in
the literature.
Table 4.9: Statistical properties of the regression models developed for boiling point.
Properties of the data set used for regression analysisUnit Kelvin Number of compounds 189
Atoms C, H Range of values 111.66 to 716.15Mean 447.88 Standard deviation (SD) 106.32
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.56 0.60 0.93 0.94
Adjusted R2 0.56 0.60 0.93 0.94RMSE 52.87 52.28 26.40 24.46
Normalized RMSE (%) 8.75 8.65 4.37 4.05Mean of Residuals 1.23E-05 3.7E-06 2.2E-06 -1.2E-06SD of Residuals 69.25 66.57 24.94 25.11
Range of Residuals -188.4 to 180.1 -208.3 to 150.8 -108.7 to 145.6 -107.8 to 147.2Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.83 0.87 0.97 0.98
Adjusted R2 0.83 0.87 0.97 0.98RMSE 41.62 37.54 16.96 15.08
Normalized RMSE (%) 6.88 6.21 2.81 2.49Mean of Residuals -2.46 1.74 0.99 -0.41SD of Residuals 44.44 38.43 17.04 15.04
Range of Residuals -203.3 to 139.4 -126.9 to 163.6 -75.9 to 68.9 -42 to 92Training Set R 0.92 0.96 0.99 0.99
Validation Set R 0.92 0.85 0.98 0.99Test Set R 0.80 0.85 0.98 0.98
Chapter 4. Correlation Development for Fuel Parameters 52
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d bo
iling
poi
nt, K
Actual boiling point, K
(a) Predicted vs. actual value for MLR 1 and ANN 1.
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d bo
iling
poi
nt, K
Actual boiling point, K
(b) Predicted vs. actual value for MLR 2 and ANN 2.
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d bo
iling
poi
nt, K
Actual boiling point, K
(c) Predicted vs. actual value for MLR 3 and ANN 3.
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d bo
iling
poi
nt, K
Actual boiling point, K
(d) Predicted vs. actual value for MLR 4 and ANN 4.
Figure 4.8: Boiling point regression analysis results.
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 Perfect fit Alkynes, Ivanciuc 1998 [153] Alkynes, Gakh et al. 1994 [152] Alkynes, Espinosa et al. 2000 [151] Chlorosilanes, Bunz et al. 1998 (MLR) [149] Chlorosilanes, Bunz et al. 1998 (ANN) [149] Alkanes + Alkenes, Espinosa et al. 2000 [151] Organic compounds, Hall and Story 1996 [154] Organic compounds, Egolf et al. 1994 [155] ANN 4
Pred
icte
d bo
iling
poi
nt, K
Actual boiling point, K
Figure 4.9: Comparison of the ANN4 boiling point model to correlations proposed in theliterature.
Chapter 4. Correlation Development for Fuel Parameters 53
4.4.4 Freezing Point Correlations
Table 4.10 summarizes the properties of the freezing point data set used for the regression
analysis and the results of this analysis. The mathematical form of the regression results
may be found in Appendix A.
Initially, MLR was used in the analysis which did not reach the required accuracy. As
evident from Figure 4.10, the MLR results have large errors, despite being able to match
some of the experimental data perfectly. Moreover, in rare cases, they provide impossible
results (a freezing point of 0 K as evident in the figures for MLR 2 and MLR 4). To
increase the accuracy and goodness of the fit, ANN models were developed. These results
fit the experimental data better than the linear models and have lower RMSE values.
The R2 values of the ANN models is similar to values cited in Table 4.7, making them
comparable to most other proposed models.
Table 4.10: Statistical properties of the regression models developed for freezing point.
Properties of the data set used for regression analysisUnit Kelvin Number of compounds 189
Atoms C, H Range of values 85.47-630.15Mean 243.37 Standard deviation (SD) 88.04
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.45 0.51 0.59 0.63
Adjusted R2 0.45 0.51 0.59 0.63RMSE 43.92 44.13 43.34 42.57
Normalized RMSE (%) 8.06 8.10 7.96 7.82Mean of Residuals -2.6E-06 1.54E-06 -1.2E-06 -3.4E-06SD of Residuals 65.24 61.67 56.04 53.40
Range of Residuals -147.6 to 305.8 -114.9 to 309.9 -131.9 to 253.9 -95.3 to 260.8Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.67 0.73 0.80 0.84
Adjusted R2 0.67 0.77 0.80 0.84RMSE 41.03 39.56 34.18 29.22
Normalized RMSE (%) 7.53 7.26 6.28 5.36Mean of Residuals -3.039 -0.52 -0.53 2.45SD of Residuals 50.65 45.97 39.00 35.37
Range of Residuals -152.3 to 301 -192.3 to 274.4 -113 to 219.9 -79 to 146Training Set R 0.79 0.86 0.90 0.93
Validation Set R 0.78 0.79 0.89 0.85Test Set R 0.93 0.87 0.81 0.90
Chapter 4. Correlation Development for Fuel Parameters 54
100 200 300 400 500 600 700
100
200
300
400
500
600
700 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d fr
eezi
ng p
oint
, K
Actual freezing point, K
(a) Predicted vs. actual value for MLR 1 and ANN 1.
0 100 200 300 400 500 600 700
0
100
200
300
400
500
600
700 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d fr
eezi
ng p
oint
, K
Actual freezing point, K
(b) Predicted vs. actual value for MLR 2 and ANN 2.
100 200 300 400 500 600 700
100
200
300
400
500
600
700 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d fr
eezi
ng p
oint
, K
Actual freezing point, K
(c) Predicted vs. actual value for MLR 3 and ANN 3.
0 100 200 300 400 500 600 700
0
100
200
300
400
500
600
700 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d fr
eezi
ng p
oint
, K
Actual freezing point, K
(d) Predicted vs. actual value for MLR 4 and ANN 4.
Figure 4.10: Freezing point regression analysis results.
4.4.5 Dynamic Viscosity Correlations
Table 4.11 summarizes the properties of the dynamic viscosity data set used in this work
and the statistics of the results obtained from the regression analysis. The predicted
values using the regression analysis are plotted against actual values in Figure 4.11. The
detailed mathematical form of these results is available in Appendix A. All dynamic
viscosities were evaluated at 298 K.
Initial regression equations developed using MLR did not achieve high enough statistical
significance. Figure 4.11 reveals that these regression results are not accurate for dynamic
viscosities less than 0.5 cP, as they produce unacceptable results (negative values for
dynamic viscosity). Hence, ANN models were developed which achieved lower errors and
Chapter 4. Correlation Development for Fuel Parameters 55
Table 4.11: Statistical properties of the regression models developed for dynamic viscos-ity.
Properties of the data set used for regression analysisUnit cP Number of compounds 45
Atoms C, H Range of values 0.0372-3.0495Mean 0.78 Standard deviation (SD) 0.67
Multiple Linear RegressionName MLR 1 MLR 2 MLR 3 MLR 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.39 0.44 0.83 0.83
Adjusted R2 0.38 0.43 0.83 0.83RMSE 0.33 0.34 0.25 0.25
Normalized RMSE (%) 11.00 11.19 8.44 8.44Mean of Residuals 1.37E-07 -1.1E-07 -4.3E-08 1.89E-08SD of Residuals 0.52 0.50 0.28 0.28
Range of Residuals -1.2 to 1.7 -1.2 to 1.7 -0.4 to 1 -0.4 to 1Artificial Neural Networks
Name ANN 1 ANN 2 ANN 3 ANN 4Inputs NMR NMR, H/C NMR, MM NMR, H/C, MMR2 0.66 0.92 0.98 0.97
Adjusted R2 0.65 0.92 0.98 0.97RMSE 0.31 0.18 0.10 0.11
Normalized RMSE (%) 10.17 5.88 3.30 3.81Mean of Residuals 3.23E-2 1.68E-2 1.857E-2 -6.22E-3SD of Residuals 0.39 0.19 0.10 0.12
Range of Residuals -1.5 to 1.2 -0.3 to 0.7 -0.3 to 0.3 -0.3 to 0.2Training Set R 0.81 0.96 0.99 0.99
Validation Set R 0.85 0.93 0.98 0.98Test Set R 0.82 0.94 0.98 0.97
better fits, reaching statistics similar to those reported in Table 4.7. The ANN models
developed do not produce negative values and match most data points perfectly.
Chapter 4. Correlation Development for Fuel Parameters 56
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 Perfect fit MLR 1 ANN 1 training set ANN 1 validation set ANN 1 testing set
Pred
icte
d dy
nam
ic v
isco
sity
, cP
Actual dynamic viscosity, cP
(a) Predicted vs. actual value for MLR 1 and ANN 1.
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 Perfect fit MLR 2 ANN 2 training set ANN 2 validation set ANN 2 testing set
Pred
icte
d dy
nam
ic v
isco
sity
, cP
Actual dynamic viscosity, cP
(b) Predicted vs. actual value for MLR 2 and ANN 2.
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 Perfect fit MLR 3 ANN 3 training set ANN 3 validation set ANN 3 testing set
Pred
icte
d dy
nam
ic v
isco
sity
, cP
Actual dynamic viscosity, cP
(c) Predicted vs. actual value for MLR 3 and ANN 3.
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 Perfect fit MLR 4 ANN 4 training set ANN 4 validation set ANN 4 testing set
Pred
icte
d dy
nam
ic v
isco
sity
, cP
Actual dynamic viscosity, cP
(d) Predicted vs. actual value for MLR 4 and ANN 4.
Figure 4.11: Dynamic viscosity regression analysis results.
Chapter 5
Application of the Correlations to
Jet Fuel and Its Surrogates
5.1 Introduction
In this chapter, the correlations developed in Chapter 4 will be applied to the jet fuel
sample and several surrogate fuels cited in the literature. This will help assess the
suitability of these surrogate fuels for different applications.
5.2 NMR Spectrum of Jet Fuel and Its Surrogates
As outlined in Chapter 4, the NMR spectrum of a chemical compound is a measure of
its chemical environment and composition. Surrogate mixtures are developed to mimic
specific properties of jet fuel. As most such properties are related to fuel chemistry, it is
reasonable to assume that surrogate fuels should have chemistry similar to the jet fuel.
Table 5.1 shows the NMR spectra of the UTIAS Jet A sample (the NMR spectrum of
which was illustrated in Chapter 4) and several surrogates proposed in the literature for
Jet A, JP-8 or kerosene (The composition of which were summarized in Table 1.1) in
terms of normalized areas under the NMR spectrum curve, H/C ratio and molecular mass.
The NMR spectra of the surrogates were estimated using their proposed formulation and
the NMR spectra of their components. Apparently, in almost all cases, surrogates have
been able to simulate the H/C ratio of jet fuel acceptability. However, half the surrogates
have molecular masses lower than that of Jet A fuel. In terms of chemical composition,
most proposed surrogates only mimic the P2, P3, P4, P5, P6 and P7 chemical shift
ranges to an acceptable extent (±5%). Unfortunately, P1 (which includes a large peak
57
Chapter 5. Application of the Correlations to Jet Fuel and Its Surrogates58
for the Jet A sample tested in this work) is underestimated by most surrogate fuels and
P12 is always over estimated. Hence, the chemical environment of these mixtures is
different from that of the jet fuel sample. Note that one of the reasons for the differences
in mimicking different shifts by these surrogates is the fact that they were developed
for modeling different aspects of the fuel. As previously mentioned, depending on the
target parameters, surrogate fuel composition might differ. Overall, the Eddings [9] and
Schultz [28] surrogates have the most similar chemical environment to the jet fuel sample,
matching several NMR spectra ranges and having similar molecular mass and H/C.
5.3 Properties of Jet Fuel and Its Surrogates
The correlations developed in the previous chapter were applied to the jet fuel sample
and the proposed surrogates. This would help to verify whether these correlations are
applicable to complex mixtures or not. It also helps assess the degree to which previous
surrogates have simulated the jet fuel properties. The result of the application of the cor-
relations to these fuels is summarized in Table 5.2. Note that the smoke points predicted
using the correlations are unreliable, as jet fuel typically has a smoke point of 21. Com-
paring surrogate fuel properties to typical properties of jet fuel, the Montgomery [29],
Drexel S-5 [26, 27], Eddings [9] and Schultz [28] surrogates have values within acceptable
ranges for the jet fuel. The results show that small deviations from actual jet fuel sample
composition may lead to huge differences in terms of cetane number, dynamic viscosity
and sooting tendency. Note that when molecular mass is included as a predictor param-
eter in the correlations, the values calculated for properties of many of these surrogates
do not match that of jet fuel. This is due to the fact that these surrogates do not have
molecular masses similar to the jet fuel.
The same properties were calculated for the mixtures based on mixture rules and are
summarized in Table 5.3. While the second half of this table suggests that the Mont-
gomery surrogate [29] best predicts average jet fuel properties, the first half contradicts it.
Overall, it seems reasonable to accept the Montgomery [29], Drexel S-5 [26, 27], Eddings
[9] and Schultz [28] surrogates as acceptable surrogates for jet fuel, capable of modeling
most target properties to an acceptable extent.
Chapter 5. Application of the Correlations to Jet Fuel and Its Surrogates59
Tab
le5.
1:N
MR
spec
tra
ofth
eJet
Asa
mple
and
seve
ral
jet
fuel
surr
ogat
es.
Par
amet
erP
1(%
)P
2(%
)P
3(%
)P
4(%
)P
5(%
)P
6(%
)P
7(%
)P
8(%
)P
12(%
)H
/CM
MU
TIA
Ssa
mple
29.4
055
.78
4.98
1.58
4.16
0.42
0.22
0.07
3.39
1.84
-2.1
153-
175
Modifi
edA
achen
[3]
12.7
161
.13
08.
454.
350
00
13.3
61.
9915
7.22
Aksi
t[5
]14
.97
49.8
32.
600
4.07
00
028
.53
1.90
134.
01E
ddin
gs[9
]16
.65
56.7
711
.31
02.
741.
900
010
.63
1.92
151.
44A
achen
[12]
15.7
261
.48
07.
363.
790
00
11.6
42.
0213
7.25
Sla
vin
skay
a[1
4]19
.32
40.1
05.
960
1.65
00
032
.97
1.73
158.
52V
ioli
[15]
19.7
849
.95
11.0
50
4.91
1.19
00
13.1
31.
9914
4.37
Dre
xel
S-5
[26,
27]
27.9
234
.90
12.0
90
11.9
70
00
23.8
91.
8115
8.92
Sch
ult
z[2
8]15
.96
57.1
03.
581.
624.
041.
190
016
.51
1.94
152.
28M
ontg
omer
y[2
9]15
.92
53.0
77.
780
1.67
00
011
.55
2.02
122.
79H
um
er[3
0]14
.22
56.4
69.
320
6.44
00
013
.56
214
3.07
JP
-8(2
2)[3
1,32
]23
.25
47.0
31.
720
14.0
00
00
14.0
01.
9814
6.20
Kah
andaw
ala
[33]
22.9
955
.63
00
3.49
00
017
.89
2.04
98.4
8
Chapter 5. Application of the Correlations to Jet Fuel and Its Surrogates60
Table 5.2: Application of the correlations developed based on NMR spectra to the jetfuel sample and surrogate fuels proposed for the jet fuel.
Correlations based on NMR only (ANN 1)
Parameter CNSP
(mm)TSI
Density(kg/m3)
DynamicViscosity
(cP)BP (K) FP (K)
UTIAS sample 45.77 118.77 26.83 742.8 0.44 375.74 176.62Modified Aachen [3] 70.10 48.63 37.09 771.1 0.70 564.91 226.94
Aksit [5] 54.01 46.55 35.49 798.8 0.63 691.16 251.05Eddings [9] 45.45 71.41 28.32 816.5 1.64 606.24 226.23Aachen [12] 66.67 81.49 34.77 761.2 0.53 497.59 215.5
Slavinskaya [14] 45.33 54.49 22.94 772.3 0.57 633.84 252.08Violi [15] 43.72 82.01 34.06 816.5 0.53 531.20 199.39
Drexel S-5 [26, 27] 40.81 105.57 13.06 750.2 0.47 389.49 202.07Schultz [28] 55.10 79.79 35.88 798.9 0.67 609.07 227.98
Montgomery [29] 45.57 92.13 27.32 795.3 1.17 594.26 226.83Humer [30] 47.93 57.88 43.66 845.2 1.72 663.78 219.27
JP-8 (22) [31, 32] 49.97 82.05 49.61 850.0 0.50 389.70 165.62Kahandawala [33] 55.93 116.71 31.30 756.4 0.52 462.12 199.91
Correlations based on NMR, H/C and MM (ANN 4)
Parameter CNSP
(mm)TSI
Density(kg/L)
DynamicViscosity
(cP)BP (K) FP (K)
UTIAS sample 43.39 7.27 26.85 810.8 1.66 463.90 233.75Modified Aachen [3] 112.92 88.62 34.62 708.9 0.81 484.74 260.48
Aksit [5] 9.93 7.27 31.80 831.0 0.72 436.90 252.25Eddings [9] 40.18 7.27 31.77 854.7 1.48 471.21 259.24Aachen [12] 106.03 88.62 26.70 699.8 0.63 448.00 240.45
Slavinskaya [14] 33.69 7.27 48.79 862.8 1.42 466.00 267.75Violi [15] 3.29 46.01 22.16 822.0 1.00 448.16 250.48
Drexel S-5 [26, 27] 37.70 46.01 33.85 842.5 1.51 460.51 251.14Schultz [28] 39.52 7.27 36.23 812.4 1.07 464.04 262.47
Montgomery [29] 30.71 8.13 16.89 748.6 0.581 429.16 216.84Humer [30] -4.37 8.05 27.11 831.5 0.93 452.71 257.83
JP-8 (22) [31, 32] 38.83 7.27 79.09 1235.1 5.98 748.51 544.81Kahandawala [33] 19.36 86.37 6.92 767.2 0.41 377.30 198.38
Chapter 5. Application of the Correlations to Jet Fuel and Its Surrogates61
Table 5.3: Properties of jet fuel surrogate fuels calculated using mixture rules.
Mixture rule applied to experimental data
Parameter CNSP
(mm)TSI
Density(kg/m3)
DynamicViscosity
(cP)BP (K) FP (K)
Modified Aachen [3] - 61.38 18.91 770.4 - 477.19 254.63Aksit [5] - 61.44 20.22 772.4 - 441.72 217.32
Eddings [9] 57.80 - - 816.3 - - -Aachen [12] - 73.94 16.44 756.8 - 446.21 240.28
Slavinskaya [14] - - - 835.3 - 489.10 236.93Violi [15] 50.20 65.17 14.42 771.7 - - -
Drexel S-5 [26, 27] 29.20 - - 960.1 - 475.96 230.98Schultz [28] 54.84 - - 786.6 - 444.77 233.32
Montgomery [29] - 55.45 13.23 757.9 0.86 395.49 194.49Humer [30] 53.66 58.32 13.56 767.3 1.11 452.01 237.07
JP-8 (22) [31, 32] - 52.26 20.118 764.0 1.02 453.95 236.13Kahandawala [33] 45.95 99.77 11.45 718.6 0.42 374.19 181.63
Mixture rules applied to data from correlations
Parameter CNSP
(mm)TSI
Density(kg/m3)
DynamicViscosity
(cP)BP (K) FP (K)
Modified Aachen [3] 93.29 67.44 33.76 738.3 1.10 471.99 104.21Aksit [5] 42.91 58.17 30.96 813.1 0.76 443.92 149.50
Eddings [9] 56.97 53.89 24.97 814.2 1.72 462.00 185.68Aachen [12] 83.07 70.07 27.70 726.3 0.72 448.92 101.87
Slavinskaya [14] 44.06 56.98 35.86 817.8 1.65 483.14 256.53Violi [15] 57.12 67.36 21.19 764.9 1.25 453.90 119.34
Drexel S-5 [26, 27] 34.07 43.95 35.34 816.2 1.71 476.91 233.94Schultz [28] 62.24 73.73 24.08 767.2 1.36 465.29 183.20
Montgomery [29] 54.29 59.67 21.90 784.0 0.85 395.83 201.24Humer [30] 62.91 63.91 26.50 752.8 1.11 453.89 61.17
JP-8 (22) [31, 32] 58.38 58.25 30.38 606.8 1.03 454.81 252.60Kahandawala [33] 46.19 100.87 11.41 750.5 0.41 378.87 46.77
Chapter 6
Surrogate Mixture Development
6.1 Introduction
In this chapter, a procedure will be presented for mixing pure compounds to form surro-
gate fuels capable of mimicking the target properties of the jet fuel. The results obtained
from this procedure are summarized at the end of this chapter and compared to Jet A
and its surrogate fuels.
6.2 Mixture Formulation Algorithm
After generating correlations between the chemical structure of compounds and their
cetane number, sooting tendency and thermophysical properties (outlined in Chapter
4), a database was created of proton NMR data of different pure compounds. This
database was used along with the correlations developed for each parameter to formulate
surrogate mixtures. Two approaches were used for analyzing mixtures and finding their
target properties:
• Approach 1.
In this approach, the correlations based on NMR spectra are used to calculate
properties of a mixture. First, we try to match the NMR spectrum of the mixture
to that of aviation jet fuel. Next, all target properties are calculated using NMR-
based correlations developed in Chapter 4 and compared to jet fuel properties. This
approach was the main focus of this work, as it has not previously been attempted.
• Approach 2.
In this approach, all mixture properties are calculated based on mixture rules. Hy-
drogen to carbon ratio and molecular mass are the only two parameters that can
62
Chapter 6. Surrogate Mixture Development 63
(to an extent) provide some information about the chemistry of the mixture. The
data set used in this analysis consisted of experimental data for the compounds.
A similar method was successfully implemented for mixture formulation and fuel
modeling for diesel fuels [21]. In this work, this approach is used to show the im-
portance of including a chemical structure parameter in surrogate fuel formulation.
6.2.1 Solution Procedure
The problem consists of choosing the components of the surrogate fuel and then finding
the molar ratios that they should be mixed at to mimic jet fuel properties. The ini-
tial database of NMR spectra prepared for this work had 270 hydrocarbons. Following
the criteria in Chapter 1 for surrogate fuel components, many of these compounds were
disqualified due to the lack of chemical kinetic mechanisms or relevant combustion prop-
erties for them. 51 compounds had the most abundant kinetic and experimental data
and had been used frequently in previous attempts at developing surrogate fuels while
184 had some form of chemical kinetic information and some experimental measurements
available. The analysis was performed on the 51 compound, 184 compounds and the full
270 compound data sets. However, only the results for the 51 compound data set will be
presented here as the surrogate fuels developed using this data set are the most useful
for practical application and include only well studied compounds. The other results,
not presented here, can be used to identify compounds for further chemical kinetic and
experimental studies in the future.
An important parameter for surrogate fuels is the number of components they are made
of. The aim of this work was to use the smallest number of components in the mixtures;
however, including the number of compounds as a parameter in the mixture develop-
ment algorithm only added computational complexity. Instead, mixture analysis was
performed for different number of components between 1-10 and then the results were
analyzed to find the best mixtures. 1-10 components is an accepted range based on the
literature review of surrogate fuels outlined in Chapter 1.
To initiate mixture development, the first approach that comes to mind is analyzing
all possible mixtures. However, the number of possible combinations is larger than the
available memory on 32 bit personal computers. Due to the fact that this work did not
have access to distributed computing facilities, an alternative approach was chosen. The
problem was formulated into an optimization-search problem and solved using optimiza-
tion algorithms in MATLAB.
In order to solve the problem using the tools in MATLAB, the problem was broken down
Chapter 6. Surrogate Mixture Development 64
into two subproblems:
• Subproblem 1: Find the best combination of components.
The components that can be used in the mixture are chosen from the database of
compounds with NMR spectra. This is a discrete problem and was solved using
the mixed-integer programming genetic algorithm (GA) implemented in MATLAB
[49]. The mixed-integer GA algorithm was chosen since it was the only global opti-
mization integer based algorithm implemented in MATLAB. The default MATLAB
setting for this algorithm were used, as they were automatically based on the in-
puts of the algorithm. Only the number of generations used by the algorithm was
changes to the multiply of the number of components used in the mixture and the
number of compounds to make sure that the algorithm automatically adapts to
increases in the size of the problem.
• Subproblem 2: Find the molar ratio of components.
The components need to be mixed to match specific properties of the fuel (NMR
spectra when approach 1 is used and fuel properties when approach 2 is used).
This was modeled as a continuous problem of minimizing the error between the
target value of the properties (which were summarized in Chapters 2 and 4) and
the calculated values by changing the molar ratio. Two constraints had to be taken
into account. The sum of the molar fractions should equal 1 and all molar fraction
should be positive. The problem was solved using MATLAB’s MultiStart algorithm
[49], which is a gradient based global optimization tool.
It should be noted that this approach to solving the problems has some limitations.
As subproblem 2 is solved inside subproblem 1, the algorithm is not highly affected by
changes to mole fractions, as it is by the components chosen. Since it seems reasonable
that the chosen components are more important than their molar ratios, this approach
seems to be acceptable for our purposes.
6.2.2 Algorithm Inputs
The target fuel properties (including the cetane number, sooting tendency (smoke point
or TSI), boiling point, freezing point, density, viscosity and the NMR spectrum in terms of
the identified NMR areas) need to be defined for the algorithm. The molecular mass and
H/C ratio can also be used as target properties and were included as inputs. Depending
on the case chosen (cases are summarized in the next section), the absolute value or
maximum and minimum values for these parameters were identified for the program.
Chapter 6. Surrogate Mixture Development 65
The NMR spectrum of the jet A fuel (illustrated in Chapter 4) was used as the target
NMR spectrum. All other properties of the target fuel were taken from Table 2.4.
As the correlations used in this work include a diversity of chemical classes, this program
can be used for developing surrogate fuels for any hydrocarbon based fuel, as long as NMR
data for that fuel and a database of compounds for use in surrogate fuel formulation are
available.
6.2.3 Definition of Different Cases
The algorithm implemented for analyzing mixtures is illustrated in Figure 6.1. Eight
different cases were implemented in the program developed for surrogate mixture formu-
lation (as shown in Figure 6.2). The cases differ in the way they use the different fuel
parameters. In some cases values within acceptable ranges were retained while in others
only values exactly matching target values were accepted. It should be noted that the
analysis was once performed using correlations only based on NMR spectra and once
using the most accurate correlations. If one of the correlations led to a result outside the
acceptable range of values (for example a negative value for freezing point in kelvins),
the next most accurate correlation was called automatically by the program. Another
notable feature is that, in the implementation used for this work, the different properties
of the fuel were not weighted. Hence, mixtures developed here can equally predict all
target properties. It is possible to add user defined weights for specific properties, if
required.
As it is evident from Figure 6.2, cases 1-6 use approach 1. They match the NMR spec-
trum of the mixture being developed to that of the aviation jet fuel. Then, they use the
correlations to find the values of the target properties and compare them to the actual
values or the range of acceptable values.
Cases 1, 2, 3 and 4 all try to match properties to their absolute values. An extra restric-
tion is added in case 2 and 4 by constraining the obtained molecular mass, H/C, sooting
tendency and dynamic viscosity values within acceptable ranges. This was done as these
parameters highly fluctuated in the surrogate fuels for jet fuel available in the literature
(as outlined in Chapter 5) and also when using the correlations.
In cases 5 and 6, all parameters are constrained within acceptable ranges and only the
NMR spectra are matched to their absolute values. As there is some unreliability in the
exact values of fuel properties (some of which were calculated using correlations), these
cases would overcome this unreliability by using well accepted ranges of values for target
properties.
Chapter 6. Surrogate Mixture Development 66
Figure 6.1: Algorithm used for surrogate mixture formulation.
Chapter 6. Surrogate Mixture Development 67
Figure 6.2: Definitions of cases for surrogate mixture formulation.
Cases 7 and 8 use approach 2, utilizing mixture rules in the analysis. Case 7 matches
fuel properties calculated using mixture rules to absolute values, while case 8 constrains
the values obtained for target parameters to acceptable ranges.
Cases 1, 2 and 5 use smoke point as the sooting tendency parameter, while cases 3, 4, 6,
7 and 8 use the TSI. As outlined in Chapter 5, the smoke point correlations seemed to be
unreliable in some cases. Hence, half the cases were based on another sooting tendency
parameter, to make sure the surrogates are capable of modeling jet fuel sooting tendency.
Obviously, this algorithm will output a specific mixture for each number of components
and case number identified. However, more detailed analysis showed that, in many cases,
mixtures developed using specific number of components better match aviation jet fuel
properties than other mixtures. Hence, the final output of the algorithm was not solely
used. Instead, all the mixtures developed during the optimization procedure were saved
and then compared to each other. The best mixtures from this pool of mixtures were
chosen as the final results of this work.
Chapter 6. Surrogate Mixture Development 68
6.3 Mixture Analysis Results
Following the procedure described in the previous section, a mixture analysis was per-
formed. About 274650 mixtures were developed for case 1, 289520 mixtures for case
2, 269180 mixtures for case 3, 279010 mixtures for case 4, 404140 mixtures for case 5,
404140 mixtures for case 6, and 29970 mixtures for case 7 and 71720 mixtures for case
8. It should be noted that most, but not all, mixtures were unique.
The surrogate fuels developed based on mixture rules where unable to compete in degree
of accuracy with surrogate fuels developed based on the correlations. It was observed
that the final results of the mixture analysis whose prime criteria was matching the value
of properties to those of jet fuel, did not always have similar chemical composition to
jet fuel as observed in the NMR spectra. Hence, the initial results were processed to
meet several criteria. Firstly, the results were filtered for surrogates capable of model-
ing the five main NMR shift ranges in the jet fuel (P1, P2, P3, P5 and P12) to ±5%.
This criterion will ensure that the surrogates are dual purpose and can be used to model
properties not taken into account in their development. Next, the results were filtered to
have CN, TSI, density, boiling point and freezing point values within acceptable ranges
for jet fuel, based on Table 2.4. Based on this analysis, it was revealed that most of the
satisfactory surrogates came from case 6. This shows that limiting target properties to
specific ranges is a more satisfactory procedure for surrogate mixture formulation that
trying to exactly match all properties of the real fuel.
Table 6.1 summarize the composition of several surrogate mixtures developed using the
procedure outlined in the previous section, in terms of the volumetric percentage of their
components. Recall from Chapter 2 that Jet A generally has about 50-65% linear and
branched alkanes, 20-30 % cycloalkanes, 10-20% aromatics and trace amounts of alkenes.
As observed in this table, most surrogates have been able to model the holistic chemical
composition of jet fuel to ±5%.
Table 6.2 compares the NMR spectra of these surrogates to the aviation jet fuel sample.
Evidently, all mixtures mimic jet fuels NMR spectrum to an acceptable extent.
Table 6.3 summarizes the target properties of the mixtures. As evident from this table,
due to the criteria taken into account in choosing the mixtures, all mixtures model avia-
tion jet fuel properties to an acceptable degree. Note that smoke point was not used as a
decisive target parameter, as the correlations seemed to be unreliable for this parameter.
Although, except surrogate 3, all other surrogates proposed here have not modeled molec-
ular mass correctly, they do have hydrogen to carbon ratios within acceptable range.
Comparing the results in Table 6.2 with those in Table 5.1 reveals that surrogates de-
Chapter 6. Surrogate Mixture Development 69
veloped in this work are able to match the chemical environment of the Jet A fuel more
accurately. Comparing results in Table 6.3 with those of Tables 5.2 and 5.3 also reveals
that surrogates developed in this work better match the typical values for most fuel
properties compared to some of the other surrogates proposed in the literature. Only
the Eddings [9] and Schultz [28] surrogates are capable of competing with surrogates
developed here in mimicking fuel chemistry and properties.
Overall, taking into account all criteria and looking at the simplest mixtures that can
mimic jet fuel, the following surrogate fuels will be recommended for future use:
1. Surrogate 1 which matches all target properties of the fuel along with its chemical
structure using the smallest number of compounds. Its only defect is not modeling
the molecular mass of jet fuel to an acceptable extent.
2. Surrogate 3 which has a small number of compounds, matches target properties
of the fuel and also models the molecular mass of the fuel correctly. The only
shortcoming of this surrogate fuel is not including any cycloalkanes which constitute
at least 10% of the jet fuel.
3. Surrogate 4 which correctly matches the fuel chemistry and target parameters while
also modeling molecular mass to an acceptable extent.
4. Surrogates 19 and 20 which, despite their larger number of compounds, model all
aspects of the fuel correctly.
Chapter 6. Surrogate Mixture Development 70
Table 6.1: Chemical composition of jet fuel surrogates developed in this work.
Number Linear and Branched Alkanes Cycloalkanes Aromatics Source
1 3-methylnonane 70.99% decalin 20.48% indane 8.53% case 6
2isododecane 10.52% decalin 13.45% propylbenzene 33.29%
case 54-methyloctane 42.73%
3n-nonane 7.29 %
- -tetralin 11.85%
case 2n-decane 46.35%isocetane 34.5%
4n-nonane 43.69% decalin 22.68% 1-methylnaphthalene 6.79%
case 6isocetane 26.84%
5n-octane 42.28%
- -tetralin 10.31%
case 6n-decane 20.66%isocetane 26.75%
6n-dodecane 28.94% decalin 23.24% propylbenzene 8.69%
case 42,6-dimethyloctane 39.13%
7n-nonane 23.08% decalin 20.91% tert-butylbenzene 10.17%
case 64-methyloctane 24.11%3-methylundecane 21.72%
8n-nonane 18.79% decalin 23.06% propylbenzene 10.02%
case 6n-dodecane 15.16%2,6-dimethyloctane 32.96%
9n-octane 17.84% decalin 21.66% 1,2-dihydronaphthalene 10.06%
case 6n-pentadecane 21.85%2,6-dimethyloctane 28.59%
10n-nonane 5.95% decalin 22.32% tetralin 6.84%
case 3n-tetradecane 4.17%3-methylnonane 60.72%
114-Methyloctane 41.35% decalin 15.87% indene 0.05%
case 33-methylundecane 30.44% phenylhexane 12.30%
12
n-octane 12.50%
- -
1,2-dihydronaphthalene 10.05%
case 6n-nonane 27.49% hexamethylbenzene 11.74%
n-undecane 16.25%isocetane 21.97%
13
n-octane 13.77% decalin 26.16% butylbenzene 7.64%
case 6n-tridecane 21.09%
3-methylundecane 5.97%2,6-dimethyloctane 25.37%
14
n-decane 19.15% decalin 15.74% 1-methylnaphthalene 7.02%
case 5n-undecane 7.44%
2,6-dimethyloctane 34.27%3-methylundecane 16.37%
15n-dodecane 28.69% decalin 24.11% benzene 1.04%
case 62,6-dimethyloctane 39.22% butylbenzene 1.40%tert-butylbenzene 5.54%
16
n-hexane 19.93%
- -
tetralin 10.32%
case 6n-nonane 13.53%
n-tetradecane 19.87%n-isocetane 21.63%
3-methylnonane 14.72%
17
n-dodecane 12.24% cyclooctane 15.10%
- - case 5isocetane 32.05% pentylcyclohexane 10.82%isooctane 9.26% butylcyclohexane 9.62%
3-methylnonane 10.91%
18
n-octane 12.76% cyclooctane 10.56% 1,2-dihydronaphthalene 10.25%
case 6n-nonane 14.02% decalin 12.15%isocetane 22.42%
3-methylundecane 17.83%
19
n-heptane 11.08% butylcyclohexane 12.88% 1,2-dihydronaphthalene 9.81%
case 5n-nonane 13.42% decalin 11.63%
n-tetradecane 19.72%isocetane 21.45%
20
n-decane 22.80% cyclooctane 7.87% 1,2-dihydronaphthalene 7.64%
case 1isocetane 16.70% pentylcyclohexane 11.28%
2,6-dimethyloctane 11.36% decalin 9.06%3-methylundecane 13.28%
Chapter 6. Surrogate Mixture Development 71
Table 6.2: NMR spectra of the proposed aviation jet fuel surrogates and Jet A fuel.
Mixture P1 (%) P2 (%) P3 (%) P4 (%) P5 (%) P6 (%) P7 (%) P8 (%) P10 (%) P11 (%) P12 (%)Jet A 29.40 55.78 4.98 1.58 4.16 0.42 0.22 0.07 - - 3.39
1 26.27 54.76 6.71 1.14 - 3.21 - - - - 7.922 25.81 54.87 8.57 - 1.34 - - - - - 9.413 30.76 51.35 - - 1.72 2.08 - - 6.79 7.28 -4 30.35 52.77 7.91 - 0.43 - - - - - 8.545 29.84 56.03 2.18 - - 3.36 - - - - 8.596 27.99 53.34 8.69 - 1.24 - - - - - 8.737 24.17 59.76 6.94 - - - - - - - 9.138 26.90 53.52 8.46 - 1.39 - - - - - 9.749 25.09 53.70 7.28 - 1.34 1.62 - - 5.29 5.68 -10 26.02 57.50 8.85 - - 2.15 - - - - 5.4911 27.44 57.08 6.23 - 1.15 - 0.01 - - - 8.0912 26.61 51.02 8.08 - 1.38 1.66 - - 5.43 5.82 -13 26.42 57.26 8.90 - 0.94 - - - - - 6.4814 28.06 57.18 5.49 - 0.44 - - - - - 8.8315 27.72 55.45 8.22 - 0.17 - - - - - 8.4416 30.58 55.13 2.20 - - 3.40 - - - - 8.6817 26.27 54.41 8.21 - 1.81 - - - - - 9.3018 24.94 56.66 4.11 - 1.38 1.66 - - 5.43 5.82 -19 26.29 50.51 8.91 - 1.38 1.66 - - 5.43 5.82 -20 25.32 56.96 6.61 - 1.07 1.29 - - 4.22 4.53 -
Table 6.3: Properties of Jet A and surrogate fuels developed in this work.
Surrogate CN SP (mm) TSIdensity(kg/m3)
BP (K) FP (K)Viscosity
(cP)MM
(g/mol)H/C
Jet A Sample 44.58 21 26.84 796.9 434.65 218.65 1.66 - -Jet A Ranges 32-57 >18 16-26 780-850 413-469 215-233 <6.5 153-175 1.84-2.1
1 42.14 8.85 16.98 789.90 436.47 227.08 1.09 138.38 1.982 42.98 46.01 19.37 791.96 439.87 223.65 1.11 143.94 1.993 38.48 7.28 23.07 784.63 430.34 223.64 1.25 159.85 1.914 42.01 21.47 22.78 816.58 439.28 219.05 1.52 149.57 1.915 44.89 46.01 16.88 786.51 437.46 226.90 1.03 141.95 2.036 42.62 46.01 18.09 789.21 440.28 220.11 1.14 145.45 2.007 44.97 7.27 18.59 781.39 433.07 218.60 1.02 138.54 2.018 42.46 46.01 16.41 790.14 432.60 217.82 1.03 139.24 1.999 39.63 7.27 20.79 786.00 419.51 218.05 1.11 144.04 1.9310 40.94 45.93 16.74 795.57 440.74 224.52 1.20 141.09 2.0111 45.68 46.01 18.68 781.22 440.44 220.91 1.08 144.87 2.0212 39.32 39.15 21.03 787.04 428.21 219.89 1.19 150.00 1.9313 42.58 46.01 18.17 789.71 441.14 219.93 1.18 143.97 2.0014 46.53 45.12 20.77 789.46 440.06 219.54 1.17 146.22 1.9915 43.44 46.01 18.85 785.34 440.53 217.68 1.16 145.87 2.0016 44.49 46.01 16.55 783.98 438.31 226.36 1.02 142.85 2.0417 42.59 46.01 17.19 790.81 435.06 221.27 1.04 140.49 2.0018 40.44 7.27 25.18 800.55 419.41 221.47 1.23 145.70 1.8919 39.34 7.33 22.86 800.84 430.47 222.27 1.33 151.71 1.9020 40.58 7.27 23.09 788.82 440.59 223.65 1.27 150.95 1.95
Chapter 7
Conclusion
Correlations were developed in Chapter 4 to relate the NMR spectra of chemical com-
pounds to their cetane number, smoke point, threshold sooting index, density, dynamic
viscosity, boiling point and freezing point. Using these correlations, mixtures were devel-
oped in Chapter 6 which (theoretically) are able to mimic properties of jet A fuel. The
proposed mixtures had 1-10 components. They were able to mimic major classes of hy-
drocarbon in aviation jet fuel and have target properties similar to Jet A fuel. Mixtures
1, 3, 4, 19 and 20 (outlined in Chapter 6 and summarized in Table 7.1) can be used as
surrogate fuels for aviation jet fuel due to their superiority in mimicking the chemistry
and other target properties of aviation jet fuel.
An analysis was also performed in Chapter 5 to assess some of the promising surro-
gate mixtures proposed in the literature. This analysis showed that the Eddings [9] and
Schultz [28] surrogates could also mimic the chemistry and target properties of jet fuel
to an acceptable extend. Hence, they are also considered acceptable jet fuel surrogates.
As previously mentioned, the surrogate mixtures proposed in this work are theoretically
verified to mimic aviation jet fuel properties. This theocratical verification is the main
limitation of this work. Experimental verification can provide more insight into the
suitability of such surrogates to practical application. Experimental verification of such
surrogates was out of the scope of this work and, thus, has been left for future researchers
to pursue.
Future work on this topic might include adding more parameters to the surrogate mixture
formulation procedure. Such parameters could include surface tension, heat capacities
and heat of combustion. Other spectroscopic techniques might also be used in develop-
ing quantitative structure-property relationships which may be used in surrogate mixture
formulation. The review of the literature also revealed that the use of two or more spec-
troscopic techniques together (for example using C-13 NMR with HPLC) may lead to
72
Chapter 7. Conclusion 73
Table 7.1: Chemical composition of the best surrogate fuels developed in this work.
Number Linear and Branched Alkanes Cycloalkanes Aromatics1 3-methylnonane 70.99% decalin 20.48% indane 8.53%
3n-nonane 7.29 %
- -tetralin 11.85%
n-decane 46.35%isocetane 34.5%
4n-nonane 43.69% decalin 22.68% 1-methylnaphthalene 6.79%isocetane 26.84%
19
n-heptane 11.08% butylcyclohexane 12.88% 1,2-dihydronaphthalene 9.81%n-nonane 13.42% decalin 11.63%
n-tetradecane 19.72%isocetane 21.45%
20
n-decane 22.80% cyclooctane 7.87% 1,2-dihydronaphthalene 7.64%isocetane 16.70% pentylcyclohexane 11.28%
2,6-dimethyloctane 11.36% decalin 9.06%3-methylundecane 13.28%
better correlations.
An approach similar to that used in developing surrogate mixtures here can be used to
formulate alternative fuels. For instance, by including measures of fuel heat capacity,
new alternative fuel mixtures can be developed for a specific target fuels.
APPENDIX 74
Appendix: Mathematical Form of the Correlations
Developed in This Work
Linear Correlations
The linear correlations developed in this work have the following general form:
f(Xk×1) = c1×kXk×1 = c1X1 + c2X2 + ...+ ckXk (7.1)
Where f(Xk×1) is the predicted value, c is a matrix of coefficients of linear regression
and X is a matrix of predictor parameters. As is evident, there is no intercept for this
equation, meaning the results are a linear combination of the predictor parameters. Table
A.1 shows the coefficients used for each correlation presented in Chapter 4. Detailed
statistical properties of these correlations are also highlighted in Chapter 4.
Neural Network Models
The neural network models have the following mathematical form:
f(Xk×1) = W1×n tanh(wn×kXk×1 + bn×1) +B (7.2)
where X is a matrix of predictor parameters, k is the number of predictor parameters
(inputs), n is the number of neurons used by the ANN, w is the input layer weight, b
is the input bias, W is the hidden layer weight and B is the hidden layer bias. Figure
A.1 shows how the MATLAB documentation depicts this function [49]. First, a linear
transformation is applied to the predictor parameters and then the hyperbolic tangent of
the results is taken. The final predicted value is a linear combination of these hyperbolic
tangent transformations, plus an intercept.
Figure A.1: The artificial neural network model as depicted by the MATLAB documen-tation [49].
APPENDIX 75
Tab
leA
.1:
Coeffi
cien
tsfo
rlinea
rco
rrel
atio
ns
pre
sente
din
Chap
ter
4.
Nam
eA
P1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
H/C
MW
(mol
/g)
Cet
ane
num
ber
ML
R1
-16.
6510
9.24
-11
.65
-3.
36-
3.36
-3.
3610
.20
10.2
010
.20
43.6
243
.62
11.0
911
.09
--
ML
R2
76.9
819
2.14
51.6
050
.38
80.6
436
.84
-10
.91
-10
.91
-10
.91
118.
7511
8.75
53.4
153
.41
-39
.08
-M
LR
3-3
0.24
66.3
5-
27.0
1-
33.5
5-
39.7
3-
36.9
3-
1.34
-1.
34-
1.34
27.0
027
.00
-22
.14
-22
.14
-0.
185
ML
R4
14.1
710
8.23
4.03
4.29
-1.
66-
15.3
5-
13.3
9-
13.3
9-
13.3
961
.05
61.0
50.
590.
59-
18.0
50.
169
Sm
oke
poi
nt
(mm
)M
LR
113
8.69
84.2
46.
74-
115.
92-
13.7
0-
5.43
17.2
617
.26
17.2
665
.30
65.3
05.
375.
37-
-M
LR
2-
98.3
3-
110.
34-
143.
75-
224.
15-
143.
00-
134.
2745
.79
45.7
945
.79
-12
2.16
-12
2.16
-97
.01
-97
.01
95.0
5-
ML
R3
153.
8111
5.21
31.0
6-
94.4
56.
8124
.32
29.5
529
.55
29.5
586
.03
86.0
330
.68
30.6
8-
-0.
203
ML
R4
-82
.34
-79
.04
-11
9.18
-20
2.58
-12
2.26
-10
4.49
57.6
857
.68
57.6
8-
100.
93-
100.
93-
71.7
2-
71.7
294
.57
-0.
198
Thre
shol
dso
otin
dex
(TSI)
indiff
usi
onflam
esM
LR
1-
1.42
12.9
112
.58
42.6
123
.71
31.9
0-
17.7
5-
17.7
5-
17.7
51.
0090
.33
74.6
374
.63
--
ML
R2
63.6
865
.93
49.8
269
.08
57.3
879
.10
-26
.86
-26
.86
-26
.86
54.0
310
5.22
102.
5010
2.50
-25
.67
-M
LR
3-
7.44
-4.
284.
7532
.31
13.4
48.
23-
23.3
1-
23.3
1-
23.3
1-
8.14
89.6
460
.77
60.7
7-
0.11
0M
LR
455
.66
47.7
741
.08
58.3
846
.48
55.0
3-
31.8
0-
31.8
0-
31.8
043
.49
104.
0488
.40
88.4
0-
24.7
60.
104
Den
sity
(kg
m3)
ML
R1
0.60
0.78
0.71
0.74
0.74
0.74
0.74
0.74
0.74
0.69
0.69
1.01
1.01
--
ML
R2
1.30
1.37
1.15
1.08
1.14
1.23
0.51
0.87
0.87
1.25
0.70
1.31
1.31
-0.
282
-M
LR
30.
570.
690.
670.
710.
700.
790.
780.
830.
830.
660.
470.
920.
92-
0.00
05M
LR
41.
221.
241.
091.
081.
081.
080.
600.
720.
721.
131.
131.
201.
20-
0.27
0.00
05B
oiling
poi
nt
(K)
ML
R1
285.
5251
0.78
344.
2533
1.80
409.
9752
6.11
354.
5572
3.57
852
2.65
329.
6216
9.66
534.
9393
1.35
--
ML
R2
528.
6170
6.41
492.
9445
8.37
561.
1861
9.62
363.
2272
1.48
561.
2550
4.74
260.
1062
4.86
958.
70-
95.2
7-
ML
R3
177.
5421
1.51
224.
1125
2.41
240.
0225
5.09
337.
7241
5.04
210.
2119
6.82
157.
2527
0.92
448.
02-
1.60
8M
LR
431
2.41
324.
7330
8.06
323.
5032
3.50
323.
5034
0.26
327.
5929
0.13
290.
1329
0.13
326.
3447
2.70
-51
.90
1.57
3F
reez
ing
poi
nt
(K)
ML
R1
156.
0323
2.96
235.
3917
7.89
242.
5133
2.16
395.
3879
8.76
853.
2816
6.31
160.
9029
2.18
883.
07-
-M
LR
242
7.50
451.
4340
1.44
319.
2441
1.37
436.
5840
5.07
796.
4289
6.39
361.
8826
1.90
392.
6191
3.61
-10
6.39
-M
LR
399
.41
76.0
517
2.40
136.
2615
3.40
190.
0638
6.56
636.
9868
9.46
96.6
815
4.39
153.
7562
9.64
-0.
843
ML
R4
322.
1226
2.85
310.
5525
3.04
295.
5928
3.91
394.
9764
6.11
735.
3625
9.08
236.
2624
4.14
671.
51-
85.7
70.
786
Dynam
icvis
cosi
ty(c
P)
ML
R1
-0.
361.
570.
88-
1.22
0.72
3.89
7.90
7.90
7.90
0.42
-0.
310.
620.
62-
-M
LR
23.
294.
383.
04-
0.08
3.03
5.98
7.98
7.98
7.98
3.08
0.72
2.01
2.01
-1.
36-
ML
R3
-0.
86-
0.97
-0.
14-
1.41
-1.
320.
654.
184.
184.
18-
1.31
0.39
-0.
79-
0.79
-0.
015
ML
R4
-0.
63-
0.78
0.00
3-
1.34
-1.
170.
794.
214.
214.
21-
1.13
0.44
-0.
69-
0.69
-0.
080.
01
APPENDIX 76
Tab
leA
.2:
Coeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
W(m
ol/g
)b
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Cet
ane
num
ber
AN
N1
-9.7
8-2
.39
1.64
9.88
9.88
9.88
-3.5
1-3
.51
-3.5
1-7
.97
-7.9
7-1
.12
-1.1
23.
320.
273.
474.
450.
02-2
.38
-3.6
6-3
.66
-3.6
60.
250.
250.
250.
250.
910.
91-2
.99
1.33
0.38
0.26
-1.3
41.
23-0
.80
-0.8
0-0
.80
0.71
0.71
0.71
-0.4
3-0
.43
-0.7
4-0
.74
2.45
-4.2
1
AN
N2
0.57
-0.3
9-1
.74
0.22
-1.2
52.
02-0
.47
-0.4
7-0
.47
0.84
0.84
2.62
2.62
0.84
0.68
-0.8
5-0
.47
-0.4
10.
41-2
.16
1.65
-2.2
4-0
.57
0.27
0.27
0.27
0.09
0.09
0.48
0.48
-2.7
9-1
.30
0.67
AN
N3
0.68
-0.2
9-1
.07
-0.6
81.
14-0
.29
-0.6
5-0
.65
-0.6
50.
970.
97-0
.10
-0.1
0-0
.06
-1.4
4-2
.16
-0.5
9-1
.20
-1.1
2-0
.23
0.16
-1.2
11.
190.
200.
200.
20-1
.02
-1.0
2-0
.79
-0.7
9-0
.19
-1.0
6-2
.17
AN
N4
-3.3
5-5
.79
-4.6
2-2
.00
6.12
1.65
-0.5
9-0
.59
-0.5
90.
770.
772.
952.
9510
.43
2.41
0.18
-0.4
80.
08-1
.41
-2.3
31.
47-1
.10
-1.2
42.
683.
443.
443.
44-0
.68
-0.6
8-4
.13
-4.1
3-2
.53
-1.3
72.
79-0
.66
Sm
oke
poi
nt
(mm
)
AN
N1
-0.9
6-2
.88
-2.4
62.
472.
472.
47-1
.91
-1.9
1-1
.91
1.28
1.28
-0.2
9-0
.29
3.19
-6.2
8
-0.8
7-1
3.47
9.62
-2.8
0-4
.03
-4.0
3-4
.03
-4.4
3-4
.43
-4.4
3-3
.34
-3.3
4-2
.60
-2.6
04.
366.
52-1
.33
0.96
3.33
-1.0
4-1
.04
-1.0
4-0
.21
-0.2
1-0
.21
1.64
1.64
-1.7
4-1
.74
-0.0
1-0
.70
3.77
0.78
-0.8
4-2
.65
-2.6
5-2
.65
-0.1
4-0
.14
-0.1
41.
851.
85-3
.09
-3.0
9-0
.55
0.83
4.33
-17.
873.
975.
355.
355.
352.
312.
312.
3116
.93
16.9
31.
401.
40-3
.08
0.21
AN
N2
-6.4
5-2
3.88
40.6
530
.99
30.9
930
.99
1.59
1.59
1.59
-5.5
2-5
.52
-0.1
8-0
.18
82.1
7-1
.27
0.23
-0.2
52.
51-2
.79
-1.8
4-1
0.23
-10.
23-1
0.23
-3.6
6-3
.66
-3.6
60.
730.
73-0
.03
-0.0
3-2
2.31
2.71
-0.6
9-0
.35
-1.8
84.
428.
318.
318.
312.
902.
902.
909.
119.
11-1
.80
-1.8
01.
89-1
.97
-0.1
9
AN
N3
0.79
0.73
0.76
-0.2
1-0
.21
-0.2
10.
350.
350.
35-0
.29
-0.2
9-0
.20
-0.2
0-1
.88
-2.4
03.
22
2.09
-1.7
00.
630.
840.
230.
230.
23-1
.25
-1.2
5-1
.25
-0.9
9-0
.99
0.39
0.39
-1.6
31.
083.
79-1
.00
-1.0
3-0
.05
1.40
1.40
1.40
-1.1
9-1
.19
-1.1
9-0
.98
-0.9
80.
550.
55-0
.58
0.69
-3.2
45.
09-1
.03
-2.9
4-0
.91
-0.9
1-0
.91
0.49
0.49
0.49
1.35
1.35
-1.2
8-1
.28
-2.3
5-1
.78
0.39
AN
N4
-14.
7414
.94
2.56
27.5
69.
658.
8810
.60
10.6
010
.60
-5.7
1-5
.71
12.3
012
.30
99.2
0-5
.34
-10.
970.
56-0
.13
-57.
4873
.56
-50.
76-2
2.63
-0.5
7-1
.78
-2.5
1-2
.51
-2.5
15.
625.
62-0
.39
-0.3
9-1
71.1
0-6
2.41
1.12
-0.2
7T
hre
shol
dso
otin
dex
(TSI)
indiff
usi
onflam
es
AN
N1
-0.3
3-0
.43
-0.0
5-0
.18
2.24
-0.0
9-0
.06
-0.0
6-0
.06
-0.4
80.
37-0
.46
-0.4
61.
801.
66
-1.1
2-0
.17
-1.4
31.
25-1
.38
-0.3
11.
380.
180.
180.
181.
21-0
.52
0.48
0.48
0.15
-0.4
5-3
.26
1.76
-1.8
11.
80-0
.43
-0.0
8-0
.66
-0.6
6-0
.66
0.30
0.81
2.95
2.95
0.69
0.17
1.85
0.70
-1.4
2-0
.19
3.77
-0.5
3-1
.12
-1.1
2-1
.12
-1.7
30.
28-3
.00
-3.0
01.
99-0
.89
AN
N2
0.35
-1.0
1-0
.73
-0.1
7-0
.17
-0.1
7-0
.31
-0.3
1-0
.31
-0.3
8-0
.38
1.93
1.93
0.50
1.34
3.59
-1.3
20.
54-0
.97
-0.5
9-0
.06
-0.0
6-0
.06
0.60
0.60
0.60
-0.2
5-0
.25
0.23
0.23
0.96
0.63
-2.6
6-1
.22
-1.8
61.
77-0
.04
-0.0
4-0
.04
-1.3
1-1
.31
-1.3
10.
940.
94-0
.33
-0.3
32.
771.
37-0
.56
1.21
-3.8
9-0
.16
2.18
2.18
2.18
-0.3
7-0
.37
-0.3
70.
670.
671.
321.
32-0
.01
1.45
0.03
AN
N3
-5.0
53.
31-0
.45
2.11
-3.1
01.
011.
651.
651.
653.
14-0
.000
41.
151.
153.
89-1
.74
-0.7
4-0
.89
-4.0
61.
13-0
.44
1.04
0.17
0.04
1.77
1.77
1.77
0.79
1.25
1.28
1.28
3.43
1.74
0.76
AN
N4
0.14
-0.6
00.
280.
070.
070.
07-0
.56
-0.5
6-0
.56
1.10
1.10
-0.2
2-0
.22
-0.1
81.
50-1
.63
1.24
-0.3
60.
34-0
.27
0.06
-0.3
6-0
.36
-0.3
60.
750.
750.
75-1
.31
-1.3
10.
001
0.00
10.
05-2
.23
0.66
1.46
-0.1
80.
460.
620.
790.
790.
791.
611.
611.
61-0
.36
-0.3
60.
810.
81-0
.58
0.68
-0.7
6-0
.38
-1.3
30.
004
-0.9
20.
003
0.00
30.
003
0.06
0.06
0.06
0.61
0.61
-0.1
5-0
.15
-0.9
82.
53-1
.67
1.16
APPENDIX 77
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
ks
pre
sente
din
chap
ter
4.
wH
/CM
W(m
ol/g
)b
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Den
sity
(kg
m3)
AN
N1
3.34
-3.2
60.
160.
940.
050.
240.
901.
261.
260.
481.
36-0
.13
-0.1
3-2
.29
-0.9
2
0.29
-0.1
41.
121.
40-1
.40
0.04
0.18
0.56
0.33
0.33
0.85
0.08
-0.7
2-0
.72
-0.8
6-1
.18
-1.2
3-0
.34
1.24
-1.2
53.
230.
210.
21-0
.57
-0.5
7-0
.67
-0.1
4-0
.96
-0.9
6-0
.05
0.13
0.64
-0.7
4-0
.76
0.38
0.86
-0.2
0-0
.31
-0.1
7-0
.17
-0.3
70.
38-0
.43
-0.4
30.
97-0
.51
-0.4
8-0
.60
0.50
1.42
-0.1
90.
28-0
.77
-0.1
0-0
.10
0.43
0.67
2.31
2.31
-2.1
22.
35
AN
N2
1.70
1.89
0.81
0.39
-1.3
2-1
.32
0.67
0.67
0.67
-0.3
2-0
.32
0.69
0.69
-5.5
9-2
.90
2.83
1.31
0.39
-0.1
1-0
.13
1.27
-0.4
6-0
.46
-1.3
1-1
.31
-1.3
10.
620.
62-0
.23
-0.2
31.
12-1
.02
0.50
0.34
0.50
0.75
0.65
0.81
0.81
-0.7
6-0
.76
-0.7
6-0
.10
-0.1
0-0
.96
-0.9
6-0
.85
0.94
1.12
-0.7
90.
93-1
.23
0.92
0.50
0.50
0.65
0.65
0.65
0.75
0.75
0.46
0.46
2.03
-0.3
20.
560.
68-2
.23
1.26
-2.0
0-2
.66
-2.6
60.
210.
210.
21-0
.69
-0.6
90.
500.
50-3
.02
0.38
0.67
1.75
-0.7
51.
22-0
.64
1.16
1.16
1.42
1.42
1.42
-0.7
4-0
.74
0.53
0.53
-2.3
50.
07-0
.77
0.12
0.14
0.25
0.73
-1.4
1-1
.41
-0.3
2-0
.32
-0.3
20.
100.
10-0
.73
-0.7
30.
22-1
.27
-1.6
90.
48-1
.06
-0.7
7-0
.54
-1.2
6-1
.26
0.25
0.25
0.25
-0.3
4-0
.34
-0.5
3-0
.53
-0.4
21.
960.
28
AN
N3
-0.1
0-0
.43
-0.4
0-0
.31
-0.3
1-0
.31
-0.0
7-0
.07
-0.0
7-0
.49
-0.4
9-1
.25
-1.2
54.
322.
501.
78
1.96
-0.8
8-1
.11
0.17
0.53
0.53
0.53
-0.4
2-0
.42
-0.4
20.
030.
03-0
.66
-0.6
60.
361.
340.
36-1
.98
-2.7
01.
201.
131.
131.
130.
920.
920.
921.
791.
792.
452.
451.
92-1
.30
0.11
-1.0
0-1
.90
-1.6
5-0
.64
-0.6
4-0
.64
-1.0
3-1
.03
-1.0
3-2
.33
-2.3
3-4
.23
-4.2
311
.00
2.92
-4.4
0-0
.02
-1.5
2-2
.11
0.39
0.39
0.39
0.65
0.65
0.65
0.17
0.17
1.28
1.28
-1.1
90.
30-0
.10
0.61
-0.2
2-3
.01
-1.4
6-1
.46
-1.4
6-1
.68
-1.6
8-1
.68
1.18
1.18
0.57
0.57
3.85
0.04
0.03
-0.1
71.
09-3
.76
-0.7
0-0
.70
-0.7
00.
320.
320.
32-2
.07
-2.0
72.
692.
691.
291.
22-0
.09
-0.0
80.
091.
99-1
.89
-1.8
9-1
.89
1.99
1.99
1.99
1.85
1.85
-0.9
6-0
.96
-2.7
40.
36-0
.07
-1.0
32.
00-1
.23
-1.0
4-1
.04
-1.0
4-0
.01
-0.0
1-0
.01
2.03
2.03
-0.7
5-0
.75
0.88
-1.3
7-0
.05
-2.4
60.
55-1
.90
0.06
0.06
0.06
-0.4
2-0
.42
-0.4
21.
151.
152.
762.
76-0
.81
-1.3
90.
11
AN
N4
-0.2
70.
491.
15-0
.61
0.65
0.65
-0.9
9-0
.99
-0.9
9-0
.80
-0.8
0-0
.22
-0.2
2-2
.99
-0.3
9-1
.48
0.11
0.95
1.35
1.31
-0.3
00.
84-0
.66
-0.6
61.
011.
011.
010.
790.
790.
830.
83-4
.23
-1.3
8-1
.94
2.69
0.63
0.96
0.48
-1.2
40.
730.
730.
820.
820.
82-0
.77
-0.7
70.
360.
360.
14-0
.81
-0.7
20.
630.
140.
280.
170.
110.
500.
500.
810.
810.
81-0
.36
-0.3
6-0
.06
-0.0
60.
95-0
.23
0.02
-0.8
8-0
.08
0.29
-0.5
5-1
.11
0.29
0.29
-0.4
8-0
.48
-0.4
8-0
.02
-0.0
2-0
.61
-0.6
10.
36-0
.25
0.90
-0.0
8-0
.10
0.09
-0.1
3-0
.46
0.09
0.09
1.15
1.15
1.15
-0.5
1-0
.51
-0.2
2-0
.22
-0.8
0-1
.28
-1.5
2-0
.80
-0.1
40.
020.
27-0
.12
-0.3
0-0
.30
-0.8
5-0
.85
-0.8
50.
840.
840.
720.
721.
26-0
.04
-1.6
4-0
.59
Dynam
icvis
cosi
ty(c
P)
AN
N1
1.11
1.14
0.99
0.53
0.53
0.53
-1.4
7-1
.47
-1.4
71.
281.
280.
660.
660.
23-5
.22
-5.2
315
.67
-7.2
2-8
.28
1.75
1.75
1.75
-1.8
4-1
.84
-1.8
4-2
.21
-2.2
1-1
.37
-1.3
71.
75-0
.51
AN
N2
-2.9
62.
701.
452.
092.
092.
090.
270.
270.
272.
382.
38-0
.64
-0.6
4-0
.62
0.29
-2.0
3-1
.83
-5.6
12.
640.
960.
690.
690.
691.
001.
001.
001.
041.
040.
360.
36-0
.33
-1.2
31.
03
AN
N3
0.06
0.28
0.15
-0.1
9-0
.19
-0.1
90.
420.
420.
42-0
.36
-0.3
6-1
.00
-1.0
02.
00-0
.82
0.64
-0.0
8-0
.72
-4.5
3-1
.24
-0.6
7-0
.67
-0.6
76.
486.
486.
48-3
.66
-3.6
61.
551.
556.
090.
390.
26A
NN
4-0
.74
-0.8
2-0
.53
0.17
-0.1
7-0
.28
-0.1
2-0
.12
-0.1
2-0
.25
0.51
0.09
0.09
1.80
-0.9
60.
20-2
.03
1.10
APPENDIX 78
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
Wb
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Boi
ling
poi
nt
(K)
AN
N1
-0.0
70.
32-2
.11
1.59
2.17
0.32
-0.3
1-0
.13
-0.0
21.
500.
770.
371.
061.
351.
48
-0.1
0
5.80
-3.6
6-6
.05
-0.1
4-2
.50
0.29
-0.3
2-0
.13
-0.4
31.
280.
341.
36-0
.37
1.47
0.72
-0.6
90.
65-2
.17
1.82
-1.2
4-3
.40
2.15
-0.5
6-0
.36
3.18
-1.1
2-4
.11
0.44
1.62
-0.7
2-0
.32
-0.5
2-0
.06
-0.7
4-0
.69
-0.3
30.
23-0
.67
-0.4
6-0
.64
-0.0
7-0
.49
-0.1
60.
450.
501.
42-2
.16
1.66
-1.3
2-0
.48
-1.0
8-0
.21
0.08
0.85
3.69
0.24
1.17
0.12
-0.4
2-0
.50
5.75
-9.4
05.
110.
23-1
.08
2.16
2.84
-0.5
6-0
.53
0.25
0.60
-2.2
6-0
.10
0.40
0.35
2.72
1.21
2.40
0.74
0.33
-0.3
50.
461.
490.
04-5
.14
0.26
2.87
-1.5
60.
45-0
.86
1.45
0.74
0.97
-0.3
6-1
.44
-4.1
13.
220.
200.
31-1
.54
-0.6
5-0
.03
0.44
-0.8
30.
75-5
.11
1.14
2.23
-1.0
7-0
.05
0.35
-1.1
80.
71-0
.29
2.13
-0.6
03.
350.
481.
490.
70
AN
N2
-1.4
0-0
.65
1.79
-0.7
40.
190.
190.
900.
900.
90-1
.45
-1.4
5-0
.50
-0.5
00.
231.
831.
01
-1.1
6
0.28
0.86
-0.1
5-0
.11
0.48
0.77
0.47
0.47
0.47
0.86
0.86
0.40
0.40
0.46
-1.2
90.
004
0.10
-0.6
40.
50-0
.27
0.47
0.15
0.13
0.13
0.13
0.95
0.95
-0.4
3-0
.43
1.04
1.25
-1.5
7-0
.02
-0.3
7-0
.02
-1.6
20.
84-0
.58
-0.2
8-0
.28
-0.2
8-0
.60
-0.6
00.
050.
052.
450.
90-0
.95
2.31
0.35
-0.2
2-0
.18
-0.7
1-0
.45
-0.4
4-0
.44
-0.4
4-1
.12
-1.1
20.
250.
250.
600.
02-1
.64
-2.5
91.
031.
051.
47-0
.17
0.48
0.13
0.13
0.13
0.22
0.22
-0.0
1-0
.01
-0.1
3-0
.37
-2.3
6-0
.98
0.35
-1.1
90.
41-0
.51
0.66
0.33
0.33
0.33
-0.9
0-0
.90
-0.0
1-0
.01
-0.0
2-0
.82
-1.0
94.
01-1
.64
-0.6
8-0
.88
0.05
-0.5
6-0
.19
-0.1
9-0
.19
-0.6
1-0
.61
0.00
40.
004
0.14
1.31
-1.0
4-1
.37
0.12
0.01
-0.2
3-0
.38
-0.1
60.
940.
940.
940.
960.
960.
230.
23-2
.54
-1.7
9-1
.32
AN
N3
1.63
1.59
-0.3
60.
920.
920.
92-0
.54
-0.5
4-0
.54
-0.5
4-0
.54
-0.2
7-0
.27
-1.5
3-2
.39
-1.6
2
-0.3
7
0.05
-0.7
4-1
.09
0.86
0.86
0.86
-0.7
1-0
.71
-0.7
11.
401.
400.
750.
751.
871.
81-0
.42
0.61
0.16
-0.3
9-0
.25
-0.2
5-0
.25
0.86
0.86
0.86
-0.3
5-0
.35
-0.0
1-0
.01
-1.5
0-1
.28
0.84
0.11
-0.1
6-0
.66
-1.7
1-1
.71
-1.7
10.
380.
380.
38-1
.99
-1.9
90.
320.
32-0
.67
1.07
-0.9
2-0
.70
1.99
2.66
-0.9
5-0
.95
-0.9
5-0
.14
-0.1
4-0
.14
0.71
0.71
1.82
1.82
-2.3
4-0
.08
0.75
-0.3
60.
081.
620.
160.
160.
161.
011.
011.
01-0
.97
-0.9
70.
760.
761.
07-0
.03
0.33
0.65
0.40
-0.2
01.
061.
061.
06-1
.11
-1.1
1-1
.11
1.27
1.27
0.60
0.60
-0.4
40.
001
-0.4
60.
180.
160.
39-0
.37
-0.3
7-0
.37
0.59
0.59
0.59
-0.2
5-0
.25
-0.0
3-0
.03
-1.2
7-0
.02
-1.0
5-0
.02
0.47
1.30
0.44
0.44
0.44
0.67
0.67
0.67
-0.4
3-0
.43
-1.3
4-1
.34
2.28
-1.6
10.
12-0
.60
1.11
1.71
0.39
0.39
0.39
0.20
0.20
0.20
-1.6
5-1
.65
0.70
0.70
-0.9
8-1
.51
-1.1
80.
560.
450.
13-0
.46
-0.4
6-0
.46
-0.8
3-0
.83
-0.8
3-0
.49
-0.4
9-2
.23
-2.2
3-0
.29
1.82
-0.1
3-0
.93
1.43
0.98
-0.8
7-0
.87
-0.8
7-0
.02
-0.0
2-0
.02
1.18
1.18
0.58
0.58
1.09
-2.2
8-0
.11
AN
N4
-0.4
1-0
.62
7.86
5.62
1.48
-3.8
9-3
.60
-1.0
6-0
.67
-4.2
1-0
.05
-2.6
01.
04-5
.65
2.24
1.62
0.27
-2.3
3
4.53
4.35
0.76
-1.1
53.
790.
700.
914.
382.
39-0
.13
2.05
-2.8
4-0
.63
-3.5
15.
01-2
.81
1.00
2.55
-5.4
8-2
.24
-3.0
6-9
.02
-4.1
20.
63-4
.31
-0.7
15.
37-1
.01
8.73
6.62
6.97
-9.1
10.
19-0
.04
1.24
0.76
0.06
0.11
0.67
-1.1
3-1
.54
-0.0
70.
500.
781.
01-0
.10
-0.0
4-5
.06
-0.7
7-0
.76
-0.4
1-0
.14
-0.0
60.
130.
02-0
.11
0.26
0.08
0.00
3-0
.08
-0.1
0-0
.02
0.12
-0.0
61.
55-0
.36
1.13
-1.3
01.
15-1
.65
-1.6
2-1
.50
-2.0
8-0
.91
-0.8
1-0
.53
-0.8
82.
75-0
.84
-0.3
10.
35-2
.63
7.00
2.18
3.76
APPENDIX 79
Tab
leA
.2(c
onti
nued
):C
oeffi
cien
tsfo
rar
tifici
alneu
ral
net
wor
km
odel
spre
sente
din
Chap
ter
4.
wH
/CM
Wb
WB
AP1
AP2
AP3
AP4
AP5
AP6
AP7
AP8
AP9
AP10
AP11
AP12
AP13
Fre
ezin
gp
oint
(K)
AN
N1
-2.8
91.
860.
08-1
.18
-2.2
31.
43-0
.21
0.95
0.51
1.11
-0.3
50.
742.
811.
510.
22
1.18
0.69
0.74
2.77
-0.4
5-3
.88
-0.2
6-0
.11
-0.2
2-0
.03
-1.4
90.
72-1
.68
0.04
1.33
-0.2
3-1
.39
-0.9
0-0
.05
-2.4
4-3
.38
11.7
81.
29-0
.49
-1.0
8-3
.80
-1.0
0-4
.36
-2.6
01.
26-1
.54
4.42
-1.4
2-3
.25
5.73
0.97
0.69
-2.4
4-0
.36
-0.0
8-3
.83
0.69
4.37
-2.4
0-0
.53
-0.2
5-8
.12
-1.1
4-2
.31
0.74
-6.7
16.
09-2
.17
-1.3
8-1
.03
-0.5
6-0
.86
8.32
-0.4
60.
69-0
.23
0.01
-1.5
1-1
.99
0.53
-2.4
12.
690.
25-0
.42
-0.1
1-4
.57
-0.8
0-1
.22
5.75
0.18
0.38
-0.9
212
.04
-9.4
35.
28-6
.30
-1.9
1-1
.67
-0.7
40.
242.
79-0
.43
2.79
1.16
-1.4
5-0
.06
3.06
4.09
-0.0
6-3
.07
0.66
4.23
0.37
0.53
0.05
-6.8
50.
69-2
.55
-0.0
4-2
.01
-0.2
5
AN
N2
-0.3
80.
37-0
.44
-0.8
00.
330.
380.
970.
970.
970.
280.
28-0
.02
-0.0
21.
28-1
.62
1.32
-0.4
5
0.45
-1.0
9-0
.04
0.56
-0.2
81.
920.
310.
310.
31-0
.90
-0.9
0-0
.50
-0.5
00.
311.
49-0
.82
0.78
2.38
0.33
1.39
-0.8
7-0
.43
1.11
1.11
1.11
-1.2
9-1
.29
0.80
0.80
-1.2
4-1
.64
-1.7
00.
47-4
.16
-0.0
021.
05-0
.62
-0.7
80.
440.
440.
440.
610.
610.
500.
50-0
.42
-0.4
00.
35-0
.62
-0.8
4-0
.04
0.71
-1.4
70.
07-0
.18
-0.1
8-0
.18
-0.4
8-0
.48
-0.3
0-0
.30
-0.7
10.
420.
13-0
.06
1.87
1.04
-0.9
0-0
.08
-1.7
4-0
.14
-0.1
4-0
.14
-0.8
4-0
.84
-0.4
1-0
.41
-1.1
4-0
.09
-1.0
4-0
.01
-1.4
21.
240.
29-0
.19
0.58
-1.1
9-1
.19
-1.1
90.
250.
25-0
.49
-0.4
90.
890.
50-0
.60
-0.0
5-2
.51
0.66
-0.1
3-0
.55
0.02
0.33
0.33
0.33
0.72
0.72
-0.2
0-0
.20
-0.5
21.
190.
551.
511.
722.
190.
39-0
.66
-0.0
4-0
.59
-0.5
9-0
.59
-1.3
1-1
.31
-0.4
6-0
.46
-3.8
71.
170.
86-0
.98
0.04
-1.7
71.
18-0
.32
-0.3
4-0
.76
-0.7
6-0
.76
0.35
0.35
-0.7
0-0
.70
-2.7
1-1
.26
-0.1
9
AN
N3
-1.8
3-0
.50
-0.6
6-0
.64
1.74
1.72
1.13
-0.2
4-0
.32
-0.9
9-0
.47
-2.1
00.
281.
53-0
.93
0.29
1.69
0.93
-1.7
30.
080.
26-0
.40
0.08
-0.1
4-0
.16
1.12
-0.4
60.
270.
780.
510.
44-0
.40
0.69
1.51
-3.9
00.
751.
143.
75-0
.81
0.66
0.53
-0.2
50.
150.
34-0
.11
0.10
-1.8
3-0
.95
-0.7
80.
241.
10-1
.89
-1.8
8-1
.76
0.47
0.71
-2.5
6-0
.09
2.26
-0.0
31.
50-0
.74
-4.0
01.
49-2
.33
AN
N4
-2.3
7-0
.69
1.90
-0.8
9-0
.95
-0.2
9-0
.09
-0.0
9-0
.09
0.36
0.36
-0.8
6-0
.86
-1.5
82.
532.
022.
07
-0.2
5
-0.7
10.
420.
01-0
.35
1.10
0.50
0.63
0.63
0.63
-0.6
3-0
.63
0.44
0.44
0.12
1.62
1.04
0.25
-1.2
90.
940.
86-2
.27
-0.8
1-0
.83
1.32
1.32
1.32
-0.6
9-0
.69
-0.1
2-0
.12
-2.4
92.
110.
44-2
.05
-0.9
40.
11-0
.95
-0.6
90.
01-0
.11
-0.0
8-0
.08
-0.0
8-0
.17
-0.1
7-0
.30
-0.3
02.
000.
080.
04-2
.44
-0.4
70.
80-0
.80
-1.5
5-0
.74
-0.0
60.
860.
860.
860.
040.
04-0
.60
-0.6
01.
381.
831.
402.
120.
84-0
.85
0.04
0.51
0.70
-0.1
71.
001.
001.
00-0
.92
-0.9
2-0
.09
-0.0
9-1
.04
-0.1
51.
35-0
.12
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